Morrey and Campanato meet Besov, Lizorkin and Triebel

Lecture Notes in Mathematics

Volumn 2005, Issue , 2010, Pages 1-292

  Yuan, Wen ^a   Sickel, Winfried ^b   Yang, Dachun ^a  

^a BEIJING NORMAL UNIVERSITY   (China)

^b FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77956580849     PISSN: 00758434     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Article

References (172)

1. D. R. Adams, A note on Choquet integrals with respect to Hausdorff capacity, In: Function spaces and applications (Lund, 1986), 115-124, Lecture Notes in Math. 1302, Springer, Berlin, 1988.
2. D. R. Adams, Choquet integrals in potential theory, Publ. Mat. 42 (1998), 3-66.
3. H. Amann, Anisotropic Function Spaces and Maximal Regularity for Parabolic Problems. Part 1: Function Spaces, J. Nečas Center for Math. Modeling, Lect. Notes 6, matfyzpress, Prague, 2009.
4. T. I. Amanov, Spaces of Differentiable Functions with Dominating Mixed Derivatives, Nauka Kaz. SSR, Alma-Ata, 1976.
5. J.-M. Angeletti, S. Mazet and P. Tchamitchian, Analysis of second order elliptic operators without boundary conditions and with VMO or Hölderian coefficients. In: Multiscale wavelet methods for PDE's, Academic Press, Boston, 1997, 495-539.
6. J. Appell and P. P. Zabrejko, Nonlinear Superposition Operators, Cambridge University Press, Cambridge, 1990.
7. R. Aulaskari, J. Xiao and R. H. Zhao, On subspaces and subsets of BMOA and U BC, Analysis 15 (1995), 101-121.
8. T. Aoki, Locally bounded linear topological space, Proc. Imp. Acad. Tokyo 18 (1942), 588-594.
9. J. Bergh and J. Löfström, Interpolation Spaces, Springer, Berlin, 1976.
10. S. N. Bernštein, On properties of homogeneous functional classes, Dokl. Acad. Nauk SSSR 57 (1947), 111-114.
11. O. V. Besov, On a family of function spaces. Embedding theorems and extensions, Dokl. Acad. Nauk SSSR 126 (1959), 1163-1165.
12. O. V. Besov, On a family of function spaces in connection with embeddings and extensions, Trudy Mat. Inst. Steklov 60 (1961), 42-81.
13. O. V. Besov, V. P. Il'in and S. M. Nikol'skij, Integral Representations of Functions and Imbedding Theorems. Vol. I+II, V. H. Winston & Sons, Washington, D. C., 1978, 1979, Transalated from the Russian. Scripta Series in Mathematics, Edited by Mitchell H. Taibleson.
14. O. V. Besov, V. P. Il'in and S. M. Nikol'skij, Integralnye predstavleniya funktsii i teoremy vlozheniya, Second edition, Fizmatlit "Nauka", Moscow, 1996.
15. B. Bojarski, Sharp maximal operators of fractional order and Sobolev imbedding inequalities, Bull. Polish Acad. Sci. Math. 33 (1985), 7-16.
16. p estimates for certain nonregular pseudodifferential operators, Comm. Partial Differential Equations 7 (1982), 1023-1033.
17. G. Bourdaud, The functional calculus in Sobolev spaces. In: Function spaces, differential operators and nonlinear analysis, Teubner-Texte Math. 133, Teubner, Stuttgart, Leipzig, 1993, 127-142.
18. G. Bourdaud, Ondelettes et espaces de Besov, Rev. Mat. Iberoamericana 11 (1995), 477-512.
19. G. Bourdaud and Y. Meyer, Fonctions qui operent sur les espaces de Sobolev, J. Funct. Anal. 97 (1991), 351-360.
20. G. Bourdaud, M. Moussai and W. Sickel, An optimal symbolic calculus on Besov algebras, Ann. I. H. Poincaré-AN 23 (2006), 949-956.
21. G. Bourdaud, M. Moussai and W. Sickel, Towards sharp superposition theorems in Besov and Lizorkin-Triebel spaces, Nonlinear Anal. 68 (2008), 2889-2912.
22. G. Bourdaud, M. Moussai and W. Sickel, Composition operators on Lizorkin-Triebel spaces, J. Funct. Anal. 259 (2010), 1098-1128.
23. M. Bownik, Atomic and molecular decompositions of anisotropic Besov spaces, Math. Z. 250 (2005), 539-571. (Pubitemid 40901888)
24. M. Bownik, Anisotropic Triebel-Lizorkin spaces with doubling measures, J. Geom. Anal. 17 (2007), 387-424.
25. M. Bownik and K.-P. Ho, Atomic and molecular decompositions of anisotropic Triebel-Lizorkin spaces, Trans. Amer. Math. Soc. 358 (2006), 1469-1510.
26. Yu. A. Brudnyi, Spaces defined by means of local approximation, Trudy Moskov. Mat. Obsc. 24 (1971), 69-132.
27. Yu. A. Brudnyi, Whitney's inequality for quasi-Banach spaces. In: Function spaces and their applications to differential equations (ed. V. Maslennikova), Izd. Ross. Univ. Druzhby Narodov, Moscow, 1992, 20-27.
28. p, Trudy Math. Inst. Steklov 150 (1979), 31-51.
29. (English transl. 1981, no. 4, 33-53.)
30. V. I. Burenkov and V. S. Guliev, Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces, Studia Math. 163 (2004), 157-176.
31. V. I. Burenkov, H. V. Guliev and V. S. Guliev, Necessary and sufficient conditions for boundedness of the fractional maximal operator in local Morrey-type spaces, Dokl. Acad. Nauk 409 (2006), 443-447.
32. V. I. Burenkov and V. S. Guliev, Necessary and sufficient conditions for boundedness of the Riesz potential in local Morrey-type spaces, Potential Anal. 30 (2009), 211-249.
33. p spaces, Adv. Math. 25 (1977), 216-225.
34. S. Campanato, Proprieta di inclusione per spaci di Morrey, Richerche Mat. 12 (1963), 67-86.
35. S. Campanato, Proprieta di hölderianita di alcune classi di funzioni, Ann. Scuola Norm. Sup. Pisa 17 (1963), 175-188.
36. S. Campanato, Proprieta di una famiglia di spazi funzionali, Ann. Scuola Norm. Sup. Pisa 18 (1964), 137-160.
37. κl, α, Ann. Scuola Norm. Sup. Pisa 18 (1964), 345-360.
38. C. Cascante, J. M. Ortega and I. E. Verbitsky, Nonlinear potentials and two weight trace inequalities for general dyadic and radial kernels, Indiana Univ. Math. J. 53 (2004), 845-882.
39. 1 and BMO on the bidisc, Ann. of Math. (2) 112 (1980), 179-201.
40. F. Chiarenza and M. Frasca, Morrey spaces and Hardy-Littlewood maximal function, Rend. Math. 7 (1987), 273-279.
41. M. Christ, The extension problem for certain function spaces involving fractional order s of differentiability, Ark. Mat. 22 (1984), 63-81.
42. p, Astérisque 77 (1980), 11-66.
43. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645.
44. 1, Canad. Math. Bull. 45 (2002), 46-59.
45. n), J. Funct. Anal. 208 (2004), 377-422.
46. G. Dafni and J. Xiao, The dyadic structure and atomic decomposition of Q spaces in several real variables, Tohoku Math. J. 57 (2005), 119-145.
47. R. A. De Vore and R. C. Sharpley, Maximal functions measuring smoothness, Mem. Amer. Math. Soc. 49 (1984), no. 293, viii+115 pp.
48. L. Diening, P. Hastö and S. Roudenko, Function spaces of variable smoothness and integrability, J. Funct. Anal. 256 (2009), 1731-1768.
49. N. Dunford and J. Schwartz, Linear Operators. I, Interscience, New York and London, 1964 (First edition, 1958).
50. A. El Baraka, An embedding theorem for Campanato spaces, Electron. J. Differential Equations 66 (2002), 1-17.
51. A. El Baraka, Function spaces of BMO and Campanato type, Proceedings of the 2002 Fez Conference on Partial Differential Equations, 109-115 (electronic), Electron. J. Differ. Equ. Conf. 9, Southwest Texas State Univ., San Marcos, TX, 2002.
52. A. El Baraka, Littlewood-Paley characterization for Campanato spaces, J. Funct. Spaces Appl. 4 (2006), 193-220.
53. p, q spaces, Funct. Appro. Comment. Math. 41 (2009), 15-40.
54. J. Duoandikoetxea, Fourier Analysis, Graduate Studies in Mathematics 29, American Mathematical Society, Providence, R. I., 2001.
55. M. Essen, S. Janson, L. Peng and J. Xiao, Q spaces of several real variables, Indiana Univ. Math. J. 49 (2000), 575-615.
56. p spaces, 0 < p > 1, J. Reine Angew. Math. 485 (1997), 173-195.
57. W. Farkas, J. Johnsen and W. Sickel, Traces of Besov-Lizorkin-Triebel spaces - a complete collection of all limiting cases, Math. Bohemica 125 (2000), 1-37.
58. W. Farkas and H.-G. Leopold, Characterisations of function spaces of generalised smoothness, Ann. Mat. Pura Appl. 185 (2006), 1-62.
59. C. Fefferman and E. M. Stein, Some maximal inequalities, Amer. J. Math. 93 (1971), 107-115.
60. p, q of Triebel-Lizorkin type: pointwise multipliers and spaces on domains, Math. Nachr. 125 (1986), 29-68.
61. J. Franke and T. Runst, Regular elliptic boundary value problems in Besov-Triebel-Lizorkin spaces, Math. Nachr. 174 (1995), 113-149.
62. M. Frazier, Y.-S. Han, B. Jawerth and G. Weiss, The T1 theorem for Triebel-Lizorkin spaces, In: Harmonic analysis and partial differential equations (El Escorial, 1987), 168-181, Lecture Notes in Math. 1384, Springer, Berlin, 1989.
63. M. Frazier and B. Jawerth, Decomposition of Besov spaces, Indiana Univ. Math. J. 34 (1985), 777-799.
64. M. Frazier and B. Jawerth, The φ-transform and applications to distribution spaces, In: Function spaces and applications (Lund, 1986), 223-246, Lecture Notes in Math. 1302, Springer, Berlin, 1988.
65. M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal. 93 (1990), 34-171.
66. M. Frazier, B. Jawerth and G. Weiss, Littlewood-Paley Theory and The Study of Function Spaces, CBMS Regional Conference Series in Mathematics 79, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1991.
67. αq, Rev. Mat. Iberoamericana 4 (1988), 41-72.
68. F. G. Friedlander and M. Joshi, Introduction to the Theory of Distributions, Cambridge University Press, Cambridge, 1998.
69. L. Grafakos, Modern Fourier Analysis, Second edition, Graduate Texts in Math. 250, Springer, New York, 2008.
70. L. Grafakos and R. H. Torres, Pseudodifferential operators with homogeneous symbols, Michigan Math. J. 46 (1999), 261-269.
71. L. I. Hedberg and Y. V. Netrusov, An axiomatic approach to function spaces, spectral synthesis, and Luzin approximation, Mem. Amer. Math. Soc. 188 (2007), no. 882, vi+97 pp.
72. J. Heinonen, Lectures on Analysis on Metric Spaces, Springer-Verlag, New York, 2001.
73. E. Hernández and G. Weiss, A First Course on Wavelets, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1996.
74. L. Hörmander, Pseduodifferential operators of type 1, 1, Comm. Partial Differential Equations 13 (1988), 1085-1111.
75. L. Hörmander, Continuity of pseduodifferential operators of type 1, 1, Comm. Partial Differential Equations 14 (1989), 231-243.
76. S. Janson, On functions with conditions on the mean oszillation, Ark. Mat. 4 (1976), 189-196.
77. p and its dyadic counterpart, In: C. Kiselman, A. Vretblad (Eds.), Complex Analysis and Differential Equations, Proceeding, Marcus Wallenberg Symposium in Honor of Matts Essén, Uppsala, 1997;
78. Acta Univ. Upsaliensis 64 (1999), 194-205.
79. B. Jawerth, The trace of Sobolev and Besov spaces if 0 < p > 1, Studia Math. 62 (1978), 65-71.
80. H. Jia and H. Wang, Decomposition of Hardy-Morrey spaces, J. Math. Anal. Appl. 354 (2009), 99-110.
81. F. John and L. Nirenberg, On functions of bounded mean oszillation, Comm. Pure Appl. Math. 14 (1961), 415-426.
82. J. Johnsen, Pointwise multiplication of Besov and Triebel-Lizorkin spaces, Math. Nachr. 175 (1995), 85-133.
83. J. Johnsen and W. Sickel, On the trace problem for Lizorkin-Triebel spaces with mixed norms, Math. Nachr. 281 (2008), 1-28.
84. J.-P. Kahane and P.-G. Lemarie-Rieuseut, Fourier Series and Wavelets, Gordon and Breach Publishers, 1995.
85. G. A. Kalyabin, Characterizations of function spaces of Besov-Lizorkin-Triebel type, Dokl. Acad. Nauk. SSSR 236 (1977), 1056-1059.
86. G. A. Kalyabin, Multiplier conditions of function spaces of Besov and Lizorkin-Triebel type, Dokl. Acad. Nauk SSSR 251 (1980), 25-26.
87. G. A. Kalyabin, The description of functions of classes of Besov-Lizorkin-Triebel type, Trudy Mat. Inst. Steklov 156 (1980), 82-109.
88. G. A. Kalyabin, Criteria of the multiplication property and the embeddings in C of spaces of Besov-Lizorkin-Triebel type, Mat. Zametki 30 (1981), 517-526.
89. H. Koch and W. Sickel, Pointwise multipliers of Besov spaces of smoothness zero and spaces of continuous functions, Rev. Mat. Iberoamericana 18 (2002), 587-626.
90. H. Kozono and M. Yamazaki, Semilinear heat equations and the Navier-Stokes equation with distributions in new function spaces as initial data, Comm. Partial Differential Equations 19 (1994), 959-1014.
91. A. Kufner, O. John and S. Fučaik, Function Spaces, Academia, Prague, 1977.
92. P. Li and Z. Zhai, Well-posedness and regularity of generalized Navier-Stokes equations in some critical Q-spaces, J. Funct. Anal. (to appear).
93. P. I. Lizorkin, Operators connected with fractional derivatives and classes of differentiable functions, Trudy Mat. Inst. Steklov 117 (1972), 212-243.
94. pθ, Trudy Mat. Inst. Steklov 131 (1974), 158-181.
95. J. Marschall, Some remarks on Triebel spaces, Studia Math. 87 (1987), 79-92.
96. J. Marschall, Nonregular pseudo-differential operators, Z. Anal. Anwendungen 1 (1996), 109-148.
97. V. G. Maz'ya and T. O. Shaposnikova, Theory of Multipliers in Spaces of Differentiable Functions, Pitman, Boston, 1985.
98. V. G. Maz'ya and T. O. Shaposnikova, Theory of Sobolev Multipliers, Springer, Berlin, 2009.
99. A. Mazzucato, Function space theory and applications to non-linear PDE, Trans. Amer. Math. Soc. 355 (2003), 1297-1369.
100. Y. Meyer, Remarques sur un théorème de J. M. Bony, Suppl. Rend. Circ. Mat. Palermo, Serie II, 1 (1981), 1-20.
101. Y. Meyer, Wavelets and Operators, Cambridge University Press, Cambridge, 1992.
102. Y. Meyer and R. Coifman, Wavelets. Calderon-Zygmund and Multilinear Operators, Cambridge University Press, Cambridge, 1997.
103. G. N. Meyers, Mean oscillation over cubes and Holder continuity, Proc. Amer. Math. Soc. 15 (1964), 717-721.
104. C. B. Morrey, On the solutions of quasi linear elliptic partial differential equations, Trans. Amer. Math. Soc. 43 (1938), 126-166.
105. A. M. Najafov, On some properties of the functions from Sobolev-Morrey type spaces, Cent. Eur. J. Math. 3 (2005), 496-507.
106. A. M. Najafov, Some properties of functions from the intersection of Besov-Morrey type spaces with dominant mixed derivatives, Proc. A. Razmadze Math. Inst. 139 (2005), 71-82.
107. p, a, κ, τW (G) with dominating mixed derivatives, Siberian Math. J. 47 (2006), 505-516.
108. Y. V. Netrusov, Theorems on traces and multipliers for functions in Lizorkin-Triebel spaces, Zapsiki Nauchnykh Seminarov POMI 200 (1992), 132-138.
109. M. V. Nevskii, Approximation of functions in Orlicz classes, In: Studies in the theory of functions of several real variables (ed. Yu. A. Brudnyi), Yaroslavl. Gos. Univ., Yaroslavl', 1984, 83-101.
110. S. M. Nikol'skij, Inequalities for entire analytic functions of finite order and their application to the theory of differentiable functions of several variables, Trudy Mat. Inst. Steklov 38 (1951), 244-278.
111. S. M. Nikol'skij, Approximation of Functions of Several Variables and Imbedding Theorems, Springer-Verlag, Berlin, 1975.
112. p, λ spaces, J. Funct. Anal. 4 (1969), 71-87.
113. Y. Peetre, Remarques sur les espaces de Besov. Le cas 0 < p < 1, C. R. Acad. Sci. Paris Sér. A-B 277 (1973), 947-950.
114. Y. Peetre, The trace of Besov spaces - a limiting case, Technical Report, Lund 1975.
115. Y. Peetre, On spaces of Triebel-Lizorkin type, Ark. Mat. 13 (1975), 123-130.
116. Y. Peetre, New Thougths on Besov Spaces, Duke University Mathematics Series, Duke University Press, Durham, 1976.
117. F. Ricci and M. Taibleson, Boundary values of harmonic functions in mixed norm spaces and their atomic structure, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 10 (1983), 1-54.
118. W. Rudin, Functional Analysis. Second edition, McGraw-Hill, Inc., New York, 1991.
119. 1, 1 in spaces of Besov and Triebel-Lizorkin type, Annals Global Analysis Geometry 3 (1985), 13-28.
120. T. Runst, Mapping properties of non-linear operators in spaces of Triebel-Lizorkin and Besov type, Anal. Math. 12 (1986), 313-346.
121. T. Runst and W. Sickel, Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations, de Gruyter Series in Nonlinear Analysis and Applications 3, Walter de Gruyter, Berlin, 1996.
122. p weights, Math. Nachr. 224 (2001), 145-180.
123. V. S. Rychkov, On restrictions and extensions of the Besov and Triebel-Lizorkin spaces with respect to Lipschitz domains, J. London Math. Soc. 60 (1999), 237-257.
124. D. Sarason, Functions of vanishing mean oscillation, Trans. Amer. Math. Soc. 207 (1975), 391-405.
125. Y. Sawano, Wavelet characterization of Besov-Morrey and Triebel-Lizorkin-Morrey spaces, Funct. Approx. Comment. Math. 38 (2008), 93-107.
126. Y. Sawano, Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces on domains, Math. Nachr. 283 (2010), 1-32.
127. Y. Sawano, Brezis-Gallouet-Wainger type inequality for Besov-Morrey spaces, Studia. Math. 196 (2010), 91-101.
128. Y. Sawano and H. Tanaka, Decompositions of Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces, Math. Z. 257 (2007), 871-905.
129. Y. Sawano, D. Yang and W. Yuan, New applications of Besov-type and Triebel-Lizorkin-type spaces, J. Math. Anal. Appl. 363 (2010), 73-85.
130. H.-J. Schmeisser, Recent developments in the theory of function spaces with dominating mixed smoothness, Proc. Conf. NAFSA-8, (ed. J. Rakosnik), Inst. Math. Acad. Sci. Prague, 2007, 145-204.
131. H.-J. Schmeisser and H. Triebel, Topics in Fourier analysis and function spaces, Akademische Verlagsgesellschaft Geest & Portig K.-G., Leipzig, 1987, (Also John Wiley, 1987).
132. A. Seeger, A note on Triebel-Lizorkin spaces, Banach Center Publ. 22, Warsaw, PWN Polish Sci. Publ. 1989, 391-400.
133. p, q < s < n/p, Annali Mat. Pura Appl. 176 (1999), 209-250.
134. W. Sickel, Pointwise multipliers for Lizorkin-Triebel spaces, Operator theory: Advances and Appl. 110 (1999), 295-321.
135. p, q type, Z. Anal. Anwendungen 14 (1995), 105-140.
136. E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, N. J., 1971.
137. R. S. Strichartz, Multipliers on fractional Sobolev spaces, J. Math. Mech. 16 (1967), 1031-1060.
138. M. H. Taibleson, On the theory of Lipschitz spaces of distributions on Euclidean n-space. I. Principal properties, J. Math. Mech. 13 (1964), 407-479.
139. M. H. Taibleson, On the theory of Lipschitz spaces of distributions on Euclidean n-space. II. Translation invariant operators, duality, and interpolation, J. Math. Mech. 14 (1965), 821-839.
140. M. H. Taibleson, On the theory of Lipschitz spaces of distributions on Euclidean n-space. III. Smoothness and integrability of Fourier tansforms, smoothness of convolution kernels, J. Math. Mech. 15 (1966), 973-981.
141. L. Tang and J. Xu, Some properties of Morrey type Besov-Triebel spaces, Math. Nachr. 278 (2005), 904-917.
142. R. H. Torres, Continuity properties of pseudodifferential operators of type 1, 1, Comm. Partial Differential Equations 15 (1990), 1313-1328.
143. R. H. Torres, Boundedness results for operators with singular kernels on distribution spaces, Mem. Amer. Math. Soc. 90 (1991), no. 442, viii+172 pp.
144. H. Triebel, Spaces of distributions of Besov type on Euclidean n-space. Duality, interpolation, Ark. Mat. 11 (1973), 13-64.
145. p, q. Quasi-Banach Algebras of functions, Ann. Mat. Pura Appl. (4) 113 (1977), 33-42.
146. H. Triebel, Spaces of Besov-Sobolev-Hardy Type, Teubner-Texte Math. 9, Teubner, Leipzig, 1978.
147. H. Triebel, Theory of Function Spaces, Birkhäuser Verlag, Basel, 1983.
148. H. Triebel, Theory of Function Spaces II, Birkhäuser Verlag, Basel, 1992.
149. H. Triebel, Fractals and Spectra, Birkhäuser Verlag, Basel, 1997.
150. H. Triebel, Theory of Function Spaces III, Birkhäuser Verlag, Basel, 2006.
151. H. Triebel, Function Spaces and Wavelets on Domains, EMS Publishing House, Zürich, 2008.
152. n), Acta Math. 148 (1982), 215-241.
153. J. Vybíral, Function spaces with dominating mixed smoothness, Diss. Math. 436 (2006), 73 pp.
154. J. Vybíral, Sobolev and Jawerth embeddings for spaces with variable smoothness and integrability, Ann. Acad. Fenn. Math. 34 (2009), 529-544.
155. H. Wallin, New and old function spaces, In: Function spaces and applications (Lund, 1986), 97-114, Lecture Notes in Math. 1302, Springer, Berlin, 1988.
156. H. Wang, Decomposition for Morrey type Besov-Triebel spaces, Math. Nachr. 282 (2009), 774-787.
157. J. M. Wilson, On the atomic decomposition for Hardy spaces, Pacific J. Math. 116 (1985), 201-207.
158. P. Wojtasczyk, A Mathematical Introduction to Wavelets, Cambridge University Press, Cambridge, 1997.
159. p spaces, Ark. Mat. 40 (2002), 383-401.
160. Z. Wu and C. Xie, Q spaces and Morrey spaces, J. Funct. Anal. 201 (2003), 282-297.
161. J. Xiao, Holomorphic Q Classes, Lecture Notes in Math. 1767, Springer, Berlin, 2001.
162. p Functions, Birkhäuser Verlag, Basel, 2006.
163. J. Xiao, Homothetic variant of fractional Sobolev space with application to Navier-Stokes system, Dyn. Partial Differ. Equ. 4 (2007), 227-245.
164. p Carleson measure problem, Adv. Math. 217 (2008), 2075-2088.
165. D. Yang and W. Yuan, A note on dyadic Hausdorff capacities, Bull. Sci. Math. 132 (2008), 500-509.
166. D. Yang and W. Yuan, A new class of function spaces connecting Triebel-Lizorkin spaces and Q spaces, J. Funct. Anal. 255 (2008), 2760-2809.
167. D. Yang and W. Yuan, New Besov-type spaces and Triebel-Lizorkin-type spaces including Q spaces, Math. Z. 265 (2010), 451-480.
168. D. Yang and W. Yuan, Dual properties of Triebel-Lizorkin-Type spaces and their applications, Z. Anal. Anwendungen (to appear).
169. D. Yang and W. Yuan, Characterizations of Besov-type and Triebel-Lizorkin-type spaces via maximal functions and local means, Nonlinear Anal. (to appear).
170. W. Yuan, Y. Sawano and D. Yang, Decompositions of Besov-Hausdorff and Triebel-Lizorkin-Hausdorff spaces and their applications, J. Math. Anal. Appl. 369 (2010), 736-757.
171. n), J. Math. Anal. Appl. 351 (2009), 428-439.
172. A. Zygmund, Smooth functions, Duke Math. J. 12 (1945), 47-76.