Operator-valued Fourier multipliers on periodic Besov spaces and applications

Proceedings of the Edinburgh Mathematical Society

Volumn 47, Issue 1, 2004, Pages 15-33

  Arendt, Wolfgang ^a   Bu, Shangquan ^b  

^a UNIVERSITY OF ULM   (Germany)

^b TSINGHUA UNIVERSITY   (China)

Author keywords

Besov spaces; Cauchy problem; Fourier multipliers; Maximal regularity; Periodic solutions

Indexed keywords

EID: 2442662590     PISSN: 00130915     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0013091502000378     Document Type: Article

References (25)

1. H. AMANN, Operator-valued Fourier multipliers, vector-valued Besov spaces and applications, Math. Nachr. 186 (1997), 5-56.
2. H. AMANN, On the strong solvability of the Navier-Stokes equation, J. Math. Fluid Mech. 2 (2000), 16-98.
3. W. ARENDT AND S. BU, The operator-valued Marcinkiewicz multiplier theorem and maximal regularity, Math. Z. 240 (2002), 311-343.
4. W. ARENDT AND S. BU, Operator-valued multiplier theorems characterizing Hilbert spaces, J. Aust. Math. Soc. A, in press.
5. W. ARENDT, C. BATTY AND S. BU, Maximal regularity and multipliers for Hölder continuous functions, Studia Math., in press.
6. J. BOURGAIN, A Hausdorff-Young inequality for B-convex Banach spaces, Pac. J. Math. 101 (1982), 255-262.
7. J. BOURGAIN, Some remarks about Banach spaces in which martingale differences are unconditional, Ark. Mat. 22 (1983), 163-168.
8. J. BOURGAIN, Vector-valued Hausdorff-Young inequalities and applications, in Geometric aspects of functional analysis (1986/87), pp. 239-249 (Springer, 1988).
9. D. BURKHOLDER, A geometric condition that implies the existence of certain singular integrals of Banach-space-valued functions, in Proc. Conf. on Harmonic Analysis in Honor of Antoni Zygmund, Chicago 1981, pp. 270-286 (Wadsworth, Belmont, CA, 1983).
10. p-spaces, in Evolution equations and their applications in physics and life science (ed. L. Weis), pp. 67-87 (Marcel Dekker, 2000).
11. PH. CLÉMENT, B. DE PAGTER, F. A. SUKOCHEV AND M. WITVLIET, Schauder decomposition and multiplier theorems, Studio Math. 138 (2000), 135-163.
12. R. E. EDWARDS, Fourier series, vol. II, Graduate Texts in Mathematics, vol. 64 (Springer, 1979).
13. M. GIRARDI AND L. WEIS, Operator-valued Fourier multiplier theorems on Besov spaces, Math. Nachr. 251 (2003), 34-51.
14. M. HIEBER, Operator-valued Fourier multipliers, in Topics in nonlinear analysis, pp. 363-380 (Birkhäuser, Basel, 1999).
15. S. KWAPIEN, Isomorphic characterizations of inner product spaces by orthogonal series with vector-valued coefficients, Studia Math. 44 (1972), 583-595 (part of a collection of articles honoring the completion by Antoni Zygmund of 50 years of scientific activity, vol. IV).
16. J. LINDENSTRAUSS AND L. TZAFRIRI, Classical Banach spaces, vol. II (Springer, 1996).
17. J. PEETRE, Sur la transformation de Fourier des fonctions à valeurs vectorielles, Rend. Sem. Mat. Univ. Padova 42 (1969), 15-26.
18. H.-J. SCHMEISSER AND H. TRIEBEL, Topics in Fourier analysis and function spaces (Wiley, 1987).
19. Z. ŠTRKALJ AND L. WEIS, On operator-valued Fourier multiplier theorems, preprint, Karlsruhe (2000).
20. H. TRIEBEL, Theory of function spaces (Birkhäuser, Basel, 1983).
21. A. VENNI, Banach spaces with the Hilbert transform property, preprint, Bologna (2002).
22. L. WEIS, Stability result for semi-groups via multiplier theorems, in Differential equations, asymptotic analysis and mathematical physics, pp. 407-411 (Akademic, Berlin, 1997).
23. p-regularity, Math. Ann. 319 (2001), 735-758.
24. p-regularity, in Evolution equations and their applications in physics and life science (ed. L. Weis), pp. 195-214 (Marcel Dekker, 2001).
25. A. ZYGMUND, Trigonometric series, vol. II (Cambridge University Press, 1959).