메뉴 건너뛰기




Volumn 83, Issue 4, 1977, Pages 569-645

Extensions of hardy spaces and their use in analysis

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84966261604     PISSN: 02730979     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9904-1977-14325-5     Document Type: Article
Times cited : (1393)

References (64)
  • 1
    • 0007420479 scopus 로고
    • p and Ll
    • MR 17, 1080
    • p and Ll', Amer. J. Math. 77 (1955), 655-656. MR 17, 1080.
    • (1955) Amer. J. Math , vol.77 , pp. 655-656
    • Boas, R.1
  • 4
    • 0000024746 scopus 로고
    • Singular integral operators and differential equations
    • MR 20 #7196
    • A. P. Calderón and A. Zygmund, Singular integral operators and differential equations, Amer. J. Math. 79 (1959), 901-921. MR 20 #7196.
    • (1959) Amer. J. Math , vol.79 , pp. 901-921
    • Calderón, A.P.1    Zygmund, A.2
  • 5
    • 34250593672 scopus 로고
    • On the existence of certain singular integrals
    • MR 14, 637
    • A. P. Calderón and A. Zygmund, On the existence of certain singular integrals, Acta Math. 88 (1952), 85-139. MR 14, 637.
    • (1952) Acta Math , vol.88 , pp. 85-139
    • Calderón, A.P.1    Zygmund, A.2
  • 6
    • 0013481319 scopus 로고
    • On higher gradients of harmonic functions
    • MR 29 #4903
    • A. P. Calderón and A. Zygmund, On higher gradients of harmonic functions, Studia Math. 24 (1964), 211-226. MR 29 #4903.
    • (1964) Studia Math , vol.24 , pp. 211-226
    • Calderón, A.P.1    Zygmund, A.2
  • 7
    • 0001029344 scopus 로고
    • Proprietà di hölderianità di alcune classi di funzioni
    • MR 27 #6119
    • S. Campanato, Proprietà di hölderianità di alcune classi di funzioni, Ann. Scuola Norm. Sup. Pisa (3) 17 (1963), 175-188. MR 27 #6119.
    • (1963) Ann. Scuola Norm. Sup. Pisa (3) , vol.17 , pp. 175-188
    • Campanato, S.1
  • 9
    • 84966237575 scopus 로고    scopus 로고
    • Ark. Mat. Astronom. Fys. 25B, no. 1, (1934), 1-5
    • F. Carlson, Une inégalité, Ark. Mat. Astronom. Fys. 25B, no. 1, (1934), 1-5.
    • Une inégalité
    • Carlson, F.1
  • 10
    • 0000133812 scopus 로고
    • p
    • MR 50 # 10784
    • p, Studia Math. 51 (1974), 269-274. MR 50 # 10784.
    • (1974) Studia Math , vol.51 , pp. 269-274
    • Coifman, R.R.1
  • 11
    • 0016285753 scopus 로고
    • Characterizations of Fourier transforms of Hardy spaces
    • R. R. Coifman, Characterizations of Fourier transforms of Hardy spaces, Proc. Nat. Acad. Sci. U. S. A. 71 (1974), no. 10, 4133-4134.
    • (1974) Proc. Nat. Acad. Sci. U. S. A , vol.71 , Issue.10 , pp. 4133-4134
    • Coifman, R.R.1
  • 12
    • 1542468307 scopus 로고
    • Singular integrals and multipliers on homogeneous spaces
    • MR 47 #9180
    • R. R. Coifman and M. de Guzmán, Singular integrals and multipliers on homogeneous spaces, Rev. Un. Mat. Argentina 25 (1970/71), 137-143. MR 47 #9180.
    • (1970) Rev. Un. Mat. Argentina , vol.25 , pp. 137-143
    • Coifman, R.R.1    de Guzmán, M.2
  • 13
    • 84966261991 scopus 로고
    • Weighted norm inequalities for maximal functions and singular integrals
    • MR 50 # 10670
    • R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241-250. MR 50 # 10670.
    • (1974) Studia Math , vol.51 , pp. 241-250
    • Coifman, R.R.1    Fefferman, C.2
  • 14
    • 0000278701 scopus 로고
    • Factorization theorems for Hardy spaces in several variables
    • R. R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. of Math. 103 (1976), 611-635.
    • (1976) Ann. of Math , vol.103 , pp. 611-635
    • Coifman, R.R.1    Rochberg, R.2    Weiss, G.3
  • 15
    • 33947600206 scopus 로고
    • On subharmonicity inequalities involving solutions of generalized Cauchy-Riemann equations
    • MR 42 #6265
    • R. R. Coifman and G. Weiss, On subharmonicity inequalities involving solutions of generalized Cauchy-Riemann equations, Studia Math. 36 (1970), 77-83. MR 42 #6265.
    • (1970) Studia Math , vol.36 , pp. 77-83
    • Coifman, R.R.1    Weiss, G.2
  • 16
    • 0010990361 scopus 로고
    • Invariant systems of conjugate harmonic functions associated with compact Lie groups
    • R. R. Coifman and G. Weiss, Invariant systems of conjugate harmonic functions associated with compact Lie groups, Studia Math. 44 (1972), 301-308.
    • (1972) Studia Math , vol.44 , pp. 301-308
    • Coifman, R.R.1    Weiss, G.2
  • 20
    • 55449114457 scopus 로고
    • A multiplier theorem for ultraspherical series
    • MR 50 # 10674
    • W. Connett and A. Schwartz, A multiplier theorem for ultraspherical series, Studia Math. 51 (1974), 51-70. MR 50 # 10674.
    • (1974) Studia Math , vol.51 , pp. 51-70
    • Connett, W.1    Schwartz, A.2
  • 21
    • 0001450194 scopus 로고
    • A unified theory of Hilbert transforms and ergodic theorems
    • (1956). MR 18, 893
    • M. Cotlar, A unified theory of Hilbert transforms and ergodic theorems, Rev. Mat. Cuyana 1 (1955), 105-167 (1956). MR 18, 893.
    • (1955) Rev. Mat. Cuyana , vol.1 , pp. 105-167
    • Cotlar, M.1
  • 22
    • 0004057858 scopus 로고    scopus 로고
    • I, Interscience, New York and London, 1964 (1st ed., 1958; MR 22 #8302)
    • N. Dunford and J. Schwartz, Linear operators. I, Interscience, New York and London, 1964 (1st ed., 1958; MR 22 #8302).
    • Linear operators
    • Dunford, N.1    Schwartz, J.2
  • 23
    • 84855348517 scopus 로고
    • Academic Press, New York, MR 42 #3552
    • p spaces, Academic Press, New York, 1970. MR 42 #3552.
    • (1970) p spaces
    • Duren, P.L.1
  • 25
    • 0003864328 scopus 로고
    • Vol. II, McGraw-Hill, New York, MR 15, 419; 34 #1565
    • A. Erdélyi et al., Higher transcendental functions, Vol. II, McGraw-Hill, New York, 1953. MR 15, 419; 34 #1565.
    • (1953) Higher transcendental functions
    • Erdélyi, A.1
  • 26
    • 0002787374 scopus 로고
    • Singular integrals with mixed homogeneity
    • MR 35 #683
    • E. B. Fabes and N. M. Riviere, Singular integrals with mixed homogeneity, Studia Math. 27 (1966), 19-38. MR 35 #683.
    • (1966) Studia Math , vol.27 , pp. 19-38
    • Fabes, E.B.1    Riviere, N.M.2
  • 27
    • 84966212359 scopus 로고    scopus 로고
    • Harmonic Analysis (Studies in Math., Vol. 13, M. Ash, Ed.), Math. Assoc, of Amer., 1976, 38-75
    • p spaces, Harmonic Analysis (Studies in Math., Vol. 13, M. Ash, Ed.), Math. Assoc, of Amer., 1976, 38-75.
    • p spaces
    • Fefferman, C.1
  • 28
    • 84966260607 scopus 로고
    • Characterizations of bounded mean oscillation
    • MR 43 #6713
    • C. Fefferman, Characterizations of bounded mean oscillation, Bull. Amer. Math. Soc. 77 (1971), 587-588. MR 43 #6713.
    • (1971) Bull. Amer. Math. Soc , vol.77 , pp. 587-588
    • Fefferman, C.1
  • 29
    • 33745325637 scopus 로고
    • p spaces of several variables
    • p spaces of several variables, Acta Math. 129 (1972), 137-193.
    • (1972) Acta Math , vol.129 , pp. 137-193
    • Fefferman, C.1    Stein, E.M.2
  • 31
    • 84980130284 scopus 로고
    • Estimates for tke decomplex and analysis on the Heisenberg group
    • G. B. Folland and E. M. Stein, Estimates for tke decomplex and analysis on the Heisenberg group, Comm. Pure Appl. Math. 27 (1974), 429-522.
    • (1974) Comm. Pure Appl. Math , vol.27 , pp. 429-522
    • Folland, G.B.1    Stein, E.M.2
  • 32
    • 0008599275 scopus 로고    scopus 로고
    • Ph.D. Thesis, Washington Univ., Missouri, 1975
    • p-spaces, Ph.D. Thesis, Washington Univ., Missouri, 1975
    • p-spaces
    • Garcia-Cuerva, J.1
  • 33
    • 84960584883 scopus 로고
    • The mean value of the modules of an analytic function
    • G. H. Hardy, The mean value of the modules of an analytic function, Proc. London Math. Soc. (2) 14 (1915), 269-277.
    • (1915) Proc. London Math. Soc. (2) , vol.14 , pp. 269-277
    • Hardy, G.H.1
  • 34
    • 0007460222 scopus 로고
    • Bounded mean oscillation and regulated martingales
    • MR 50 #5930
    • C. Herz, Bounded mean oscillation and regulated martingales, Trans. Amer. Math. Soc. 193 (1974), 199-215. MR 50 #5930.
    • (1974) Trans. Amer. Math. Soc , vol.193 , pp. 199-215
    • Herz, C.1
  • 36
    • 51649136534 scopus 로고
    • Estimates for translation invariant operators in If spaces
    • MR 22 #12389
    • L. Hörmander, Estimates for translation invariant operators in If spaces, Acta Math. 104 (1960), 93-140. MR 22 #12389.
    • (1960) Acta Math , vol.104 , pp. 93-140
    • Hörmander, L.1
  • 37
    • 84972557858 scopus 로고
    • An extension of the interpolation theorem of Marcinkiewicz
    • MR 28 # 1431
    • S. Igari, An extension of the interpolation theorem of Marcinkiewicz. II, Tôhoku Math. J. (2) 15 (1963), 343-358. MR 28 # 1431.
    • (1963) II, Tôhoku Math. J. (2) , vol.15 , pp. 343-358
    • Igari, S.1
  • 38
    • 84980082306 scopus 로고
    • On functions of bounded mean oscillation
    • MR 24 #A1348
    • F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure AppL Math. 14 (1961), 415-426. MR 24 #A1348.
    • (1961) Comm. Pure AppL Math , vol.14 , pp. 415-426
    • John, F.1    Nirenberg, L.2
  • 39
    • 0004480122 scopus 로고
    • A class of singular integrals
    • MR 28 #4308
    • B. F. Jones, Jr., A class of singular integrals, Amer. J. Math. 86 (1964), 441-462. MR 28 #4308.
    • (1964) Amer. J. Math , vol.86 , pp. 441-462
    • Jones, B.F.1
  • 40
    • 0000651893 scopus 로고
    • Intertwining operators for semì-simple Lie groups
    • A. W. Knapp and E. M. Stein, Intertwining operators for semì-simple Lie groups, Ann. of Math. (2) 93 (1971), 489-578.
    • (1971) Ann. of Math. (2) , vol.93 , pp. 489-578
    • Knapp, A.W.1    Stein, E.M.2
  • 41
    • 84910927511 scopus 로고
    • Singular integrals and the principal series
    • MR 41 #8588
    • A. W. Knapp and E. M. Stein, Singular integrals and the principal series. I, Proc. Nat. Acad. Sci. U.S. A. 63 (1969), 281-284. MR 41 #8588.
    • (1969) I, Proc. Nat. Acad. Sci. U.S. A , vol.63 , pp. 281-284
    • Knapp, A.W.1    Stein, E.M.2
  • 42
    • 0000869540 scopus 로고
    • Singular integrals on homogeneous spaces and some problems of classical analysis
    • A. Korányi and S. Vági, Singular integrals on homogeneous spaces and some problems of classical analysis, Ann. Scuola Norm. Sup. Pisa 25 (1971), 575-648.
    • (1971) Ann. Scuola Norm. Sup. Pisa , vol.25 , pp. 575-648
    • Korányi, A.1    Vági, S.2
  • 43
    • 34247502417 scopus 로고
    • Distributions quasi homogènes. Généralisations des intégrals singulières et du calcul symbolique de Calderόn-Zygmund
    • MR 32 #6211
    • P. Krée, Distributions quasi homogènes. Généralisations des intégrals singulières et du calcul symbolique de Calderόn-Zygmund, C. R. Acad. Sci. Paris 261 (1965), 2560-2563. MR 32 #6211.
    • (1965) C. R. Acad. Sci. Paris , vol.261 , pp. 2560-2563
    • Krée, P.1
  • 44
    • 67349261236 scopus 로고
    • Functions regular in the half-plane
    • (Russian)
    • V. Krylov, Functions regular in the half-plane, Sbornik 6 (1939), 95-138. (Russian)
    • (1939) Sbornik , vol.6 , pp. 95-138
    • Krylov, V.1
  • 46
    • 84966205118 scopus 로고
    • Mean oscillation over cubes and Hölder continuity
    • MR 29 #5969
    • N. G. Meyers, Mean oscillation over cubes and Hölder continuity, Proc. Amer, Math. Soc, 15 (1964), 717-721. MR 29 #5969.
    • (1964) Proc. Amer, Math. Soc , vol.15 , pp. 717-721
    • Meyers, N.G.1
  • 47
    • 84968515925 scopus 로고
    • Classical expansions and their relation to conjugate harmonic functions
    • MR 33 #7779
    • B. Muckenhoupt and E. M. Stein, Classical expansions and their relation to conjugate harmonic functions, Trans. Amer. Math. Soc. 118 (1965), 17-92. MR 33 #7779.
    • (1965) Trans. Amer. Math. Soc , vol.118 , pp. 17-92
    • Muckenhoupt, B.1    Stein, E.M.2
  • 48
    • 67349220640 scopus 로고
    • Sur les valeurs moyennes du module des fonctions harmoniques et des fonctions analytiques
    • F. Riesz, Sur les valeurs moyennes du module des fonctions harmoniques et des fonctions analytiques, Acta Sci. Math. 1 (1922/23), 27-32.
    • (1922) Acta Sci. Math , vol.1 , pp. 27-32
    • Riesz, F.1
  • 49
    • 0000982510 scopus 로고
    • Singular integrals and multiplier operators
    • N. M. Rivière, Singular integrals and multiplier operators, Ark. Mat. 9 (1971), no. 2, 243-278.
    • (1971) Ark. Mat , vol.9 , Issue.2 , pp. 243-278
    • Rivière, N.M.1
  • 52
    • 84946916764 scopus 로고
    • Functions of vanishing mean oscillation
    • D. Sarason, Functions of vanishing mean oscillation, Trans. Amer. Math. Soc. 207 (1975), 391-405.
    • (1975) Trans. Amer. Math. Soc , vol.207 , pp. 391-405
    • Sarason, D.1
  • 53
    • 0002540844 scopus 로고
    • Note on the class L
    • MR 40 # 799
    • E. M. Stein, Note on the class L log L, Studia Math. 32 (1969), 305-310. MR 40 # 799.
    • (1969) Log L, Studia Math , vol.32 , pp. 305-310
    • Stein, E.M.1
  • 54
    • 1842478211 scopus 로고
    • p, multiplicateurs et fonctions de Littlewood-Paley
    • ibid. 264 (1967), A107-A108. MR 37 #695a, b, c
    • p, multiplicateurs et fonctions de Littlewood-Paley, C. R. Acad. Sci. Paris Sér. A-B 263 (1966), A716-A719, A780-A781; ibid. 264 (1967), A107-A108. MR 37 #695a, b, c.
    • (1966) C. R. Acad. Sci. Paris Sér. A-B , vol.263
    • Stein, E.M.1
  • 59
    • 51249193197 scopus 로고
    • On the theory of harmonic functions of several variables
    • MR 22 #12315
    • E. M. Stein and G. Weiss, On the theory of harmonic functions of several variables. I, Acta Math. 103 (1960), 25-62. MR 22 #12315.
    • (1960) I, Acta Math , vol.103 , pp. 25-62
    • Stein, E.M.1    Weiss, G.2
  • 60
    • 0000467298 scopus 로고
    • Generalization of the Cauchy-Riemann equations and representations of the rotation group
    • MR 36 #6540
    • E. M. Stein and G. Weiss, Generalization of the Cauchy-Riemann equations and representations of the rotation group, Amer. J. Math. 90 (1968), no. 1, 163-196. MR 36 #6540.
    • (1968) Amer. J. Math , vol.90 , Issue.1 , pp. 163-196
    • Stein, E.M.1    Weiss, G.2
  • 62
    • 84925245753 scopus 로고
    • Complex methods in harmonic analysis
    • MR 41 #5886
    • G, Weiss, Complex methods in harmonic analysis, Amer. Math. Monthly 77 (1970), no. 5, 465-474. MR 41 #5886.
    • (1970) Amer. Math. Monthly , vol.77 , Issue.5 , pp. 465-474
    • Weiss, G.1
  • 63
    • 84973999973 scopus 로고
    • Harmonic analysis
    • Math. Assoc, of Amer., Buffalo, N. Y.; Prentice-Hall, Englewood Cliffs, N. J., MR 32 #1080
    • G, Weiss, Harmonic analysis, Studies in real and complex analysis (Studies in Math., Vol. III), Math. Assoc, of Amer., Buffalo, N. Y.; Prentice-Hall, Englewood Cliffs, N. J., 1965, pp. 124-178. MR 32 #1080.
    • (1965) Studies in real and complex analysis (Studies in Math) , vol.3 , pp. 124-178
    • Weiss, G.1
  • 64
    • 84953751498 scopus 로고
    • 2nd. rev. ed., Vols. I, II, Cambridge Univ. Press, New York, MR 21 #6498
    • A. Zygmund, Trigonometric series, 2nd. rev. ed., Vols. I, II, Cambridge Univ. Press, New York, 1959. MR 21 #6498.
    • (1959) Trigonometric series
    • Zygmund, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.