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On operator-valued Fourier multiplier theorems
Author(s):
Zeljko
Strkalj;
Lutz
Weis
Journal:
Trans. Amer. Math. Soc.
359
(2007),
3529-3547.
MSC (2000):
Primary 42B15, 42A45, 46E40;
Secondary 46B09
Posted:
March 20, 2007
MathSciNet review:
2302504
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References |
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Additional information
Abstract:
The classical Fourier multiplier theorems of Marcinkiewicz and Mikhlin are extended to vector-valued functions and operator-valued multiplier functions on  or  which satisfy certain  -boundedness conditions.
References:
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- S. Blunck, Maximal regularity of discrete and continuous time evolution equations, Studia Math. 146 (2001), 157-176. MR 1853519 (2002g:34125)
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- D. Burkholder, A geometric condition that implies the existence of certain singular integrals of Banach-space-valued functions, Proc. of Conf. on Harmonic Analysis in Honor of Antoni Zygmund, Chicago 1981, Wadsworth Publishers, Belmont, Calif., 1983, 270-286. MR 0730072 (85i:42020)
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- Ph. Clément, B. de Pagter, F.A. Sukochev and H. Witvliet, Schauder Decompositions and Multiplier Theorems, Studia Mathematica 138 (2000), 135-163. MR 1749077 (2002c:47036)
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- J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II (Function Spaces), Springer-Verlag 1979. MR 0540367 (81c:46001)
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- -, Some results on Banach spaces without local unconditional structure, Comp. Math. 37 (1978), 3-19. MR 0501916 (80e:46012)
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 -regularity, Math. Ann. 319 (2001), 735-758. MR 1825406 (2002c:42016) - [Zi]
- F. Zimmermann, On vector-valued Fourier multiplier theorems, Studia Mathematica, T. XCIII (1989), 201-222. MR 1030488 (91b:46031)
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Additional Information:
Zeljko
Strkalj
Affiliation:
Institute of Mathematics I, University of Karlsruhe, Englerstrasse 2, D-76128 Karlsruhe, Germany
Email:
zeljko.strkalj@math.uni-karlsruhe.de
Lutz
Weis
Affiliation:
Institute of Mathematics I, University of Karlsruhe, Englerstrasse 2, D-76128 Karlsruhe, Germany
Email:
lutz.weis@math.uni-karlsruhe.de
DOI:
10.1090/S0002-9947-07-04417-0
PII:
S 0002-9947(07)04417-0
Received by editor(s):
October 1, 1999
Received by editor(s) in revised form:
April 10, 2003
Posted:
March 20, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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