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Fourier Multipliers and Littlewood‐Paley for modulation spaces
Author(s) -
Mohanty Parasar,
Shrivastava Saurabh
Publication year - 2014
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.201200133
Subject(s) - modulation space , mathematics , bounded function , fourier transform , context (archaeology) , extension (predicate logic) , fourier series , multiplier (economics) , fourier analysis , space (punctuation) , operator (biology) , pure mathematics , mathematical analysis , paleontology , linguistics , philosophy , biochemistry , chemistry , repressor , computer science , transcription factor , gene , biology , programming language , macroeconomics , economics
In this paper we have studied Fourier multipliers and Littlewood‐Paley square functions in the context of modulation spaces. We have also proved that any bounded linear operator from modulation spaceM p , q( R n ) , 1 ≤ p , q ≤ ∞ , into itself possesses an l 2 ‐valued extension. This is an analogue of a well known result due to Marcinkiewicz and Zygmund on classical L p ‐spaces.