Operator-valued Fourier multiplier theorems on Besov spaces

Mathematische Nachrichten

Volumn 251, Issue , 2003, Pages 34-51

  Girardi, Maria ^a,b   Weis, Lutz ^b  

^a UNIVERSITY OF SOUTH CAROLINA   (United States)

^b UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037235531     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.200310029     Document Type: Article

References (31)

1. H. Amann, Elliptic operators with infinite-dimensional state space, J. Evol. Equ. 1, No. 2, 143 -188 (2001).
2. H. Amann, Operator-valued Fourier multipliers, vector-valued Besov spaces, and applications, Math. Nachr. 186, 5-56 (1997).
3. W. Arendt, Ch. Batty, M. Hieber, and F. Neubrander, Vector-valued Laplace Transforms and Cauchy Problems (Birkhäuser, Basel, 2001).
4. W. Arendt and S. Bu, The operator-valued Marcinkiewicz multiplier theorem and maximal regularity, Math. Z. 240, No. 2, 311-343 (2002).
5. J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Grundlehren der Mathematischen Wissenschaften No. 223 (Springer-Verlag, Berlin, 1976).
6. S. Blunck, Maximal regularity of discrete and continuous time evolution equations, Studia Math. 146, No. 2, 157-176 (2001).
7. J. Bourgain, A Hausdorff-Young inequality for B-convex Banach spaces, Pacific J. Math. 101, No. 2, 255-262 (1982).
8. 1-BMO duality, in: Probability Theory and Harmonic Analysis (Cleveland, Ohio, 1983), (Dekker, New York, 1986), pp. 1-19.
9. J. Bourgain, Vector-valued Hausdorff-Young inequalities and applications, in: Geometric Aspects of Functional Analysis (1986/87) (Springer-Verlag, Berlin, 1988), pp. 239-249.
10. p-spaces, in: Proceedings of the Sixth International Conference on Evolution Equations and their Applications in Physical and Life Science, edited by Günter Lummer and Lutz Weis, Bad Herrenalb, 1998 (Marcel Dekker, New York, 2001), pp. 67-87.
11. J. Diestel and J. J. Uhl, Jr., Vector Measures, American Mathematical Society (Providence, R.I., 1977), with a foreword by B. J. Pettis, Mathematical Surveys No. 15.
12. M. Girardi and L. Weis, Integral operators with operator-valued kernels, in preparation.
13. p(X) and geometry of Banach spaces, to appear in J. Funct. Anal.
14. R. Haller, H. Heck, and A. Noll, Mikhlin's theorem for operator-valued Fourier multipliers on n-dimensional domains, Math. Nachr. 244, 110-130 (2002).
15. M. Hieber, A characterization of the growth bound of a semigroup via Fourier multipliers, in: Proceedings of the Sixth International Conference on Evolution Equations and their Applications in Physical and Life Science, edited by Günter Lummer and Lutz Weis, Bad Herrenalb, 1998 (Marcel Dekker, New York, 2001), pp. 121-124.
16. M. Hieber, Operator valued Fourier multipliers, in: Topics in Nonlinear Analysis (Birkhäuser, Basel, 1999), pp. 363-380.
17. H. König, On the Fourier-coefficients of vector-valued functions, Math. Nachr. 152, 215-227 (1991).
18. p-regularity for second order elliptic operators with uniformly continuous coefficients on domains, submitted.
19. S. Kwapień, Isomorphic characterizations of inner product spaces by orthogonal series with vector valued coefficients, Studia Math. 44, 583-595 (1972), Collection of articles honoring the completion by Antoni Zygmund of 50 years of scientific activity, VI.
20. Y. Latushkin and F. Räbiger, Fourier multipliers in stability and control theory, preprint.
21. T. R. McConnell, On Fourier multiplier transformations of Banach-valued functions, Trans. Amer. Math. Soc. 285 (1984), No. 2, 739-757.
22. J. Peetre, Sur la transformation de Fourier des fonctions á valeurs vectorielles, Rend. Sem. Mat. Univ. Padova 42, 15-26 (1969).
23. A. Pełczyński and M. Wojciechowski, Molecular decompositions and embedding theorems for vector-valued Sobolev spaces with gradient norm, Studia Math. 107, No. 1, 61-100 (1993).
24. H.-J. Schmeisser, Vector-valued Sobolev and Besov spaces, in: Seminar Analysis of the Karl-Weierstraß-Institute of Mathematics 1985/86 (Berlin, 1985/86) (Teubner, Leipzig, 1987), pp. 4-44.
25. B.-W. Schulze, Boundary Value Problems and Singular Pseudo-differential Operators (John Wiley & Sons Ltd., Chichester, 1998).
26. Ž. Štrkalj and L. Weis, On operator-valued Fourier multiplier theorems, submitted.
27. p-regularity, in: Proceedings of the Sixth International Conference on Evolution Equations and their Applications in Physical and Life Science, edited by Günter Lummer and Lutz Weis, Bad Herrenalb, 1998 (Marcel Dekker, New York, 2001), pp. 195-214.
28. p-regularity, Math. Ann. 319, No. 4, 735-758 (2001).
29. L. Weis, Stability theorems for semi-groups via multiplier theorems, in: Differential Equations, Asymptotic Analysis, and Mathematical Physics, (Potsdam, 1996), (Akademie Verlag, Berlin, 1997), pp. 407-411.
30. F. Zimmermann, On vector-valued Fourier multiplier theorems, Studia Math. 93, No. 3, 201 -222 (1989).
31. J. Garcia-Cuerva, K. S. Kazarian, V. I. Kolyada, and J. L. Torrea, Vector-valued Hausdorff-Young inequality with and applications, Uspekhi Mat. Nauk 53, No. 3(321), 3-84 (1998).