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Mikhlin's Theorem for Operator–Valued Fourier Multipliers in n Variables
Author(s) -
Haller Robert,
Heck Horst,
Noll André
Publication year - 2002
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 - 10.1002/1522-2616(200210)244:1<110::aid-mana110>3.0.co;2-s
Subject(s) - mathematics , multiplier (economics) , bounded function , operator (biology) , norm (philosophy) , pure mathematics , bounded operator , bounded variation , fourier series , discrete mathematics , mathematical analysis , biochemistry , chemistry , repressor , gene , transcription factor , political science , law , economics , macroeconomics
An operator–valued Mikhlin theorem is proved for multipliers of the form M : ℝ n → ℒ( X , Y ) where X and Y are UMD spaces. The usual norm bounds of the classical Mikhlin condition are replaced by R–bounds. Furthermore, the concept of R–bounded variation is introduced to generalize the Marcinkiewicz Fourier multiplier Theorem to the operator–valued setting.