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Multipliers on Banach spaces of functions on a locally compact Abelian group
Author(s) -
Petkova Violeta
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm002
Subject(s) - mathematics , abelian group , locally compact space , banach space , pure mathematics , group (periodic table) , bounded function , morphism , discrete mathematics , mathematical analysis , physics , quantum mechanics
Let E be a Banach space of functions on a locally compact Abelian group G satisfying certain conditions. It has been proved that for every bounded operator M on E commuting with translations there existsh M ∈ L ∞ (G E˜ ) such thatM f ˜ = h Mf ˜ ∀ f ∈ C c ( G ) , whereG E˜is a suitable subset of the group of the continuous morphisms from G into ℂ* andG ˜is a generalized Fourier transform of g defined onG E˜ .