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Fourier embeddings and Mihlin-type multiplier theorems

✍ Scribed by Tuomas Hytönen

Publisher: John Wiley and Sons
Year: 2004
Tongue: English
Weight: 395 KB
Volume: 274-275
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200310203

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✦ Synopsis

Abstract

Recent theorems on singular convolution operators are combined with new Fourier embedding results to prove strong multiplier theorems on various function spaces (including Besov, Lebesgue–Bôchner, and Hardy). All the results apply to operator‐valued multipliers acting on vector‐valued functions, but some of them are new even in the scalar case. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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## Abstract Presented is a general Fourier multiplier theorem for operator–valued multiplier functions on vector–valued Besov spaces where the required smoothness of the multiplier functions depends on the geometry of the underlying Banach space (specifically, its Fourier type). The main result cov