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Operator–valued Fourier multiplier theorems on Besov spaces
Author(s) -
Girardi Maria,
Weis Lutz
Publication year - 2003
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310029
Subject(s) - multiplier (economics) , mathematics , fourier transform , banach space , mathematical analysis , pure mathematics , operator (biology) , besov space , interpolation space , functional analysis , economics , macroeconomics , biochemistry , chemistry , repressor , gene , transcription factor
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 covers many classical multiplier conditions, such as Mihlin and Hörmander conditions.