Banach algebra of the Fourier multipliers on weighted Banach function spaces

被引：6
|
作者：
Karlovich, Alexei [1 ]
机构：
[1] Univ Nova Lisboa, Fac Ciencias & Tecnol, Ctr Matemat & Aplicacoes, Dept Matemat, P-2829516 Caparica, Portugal
来源：
CONCRETE OPERATORS | 2015年 / 2卷 / 01期
关键词：
Fourier convolution operator; Fourier multiplier; Banach function space; Cauchy singular integral operator; rearrangement-invariant space; variable Lebesgue space; Muckenhoupt-type weight;
D O I：
10.1515/conop-2015-0001
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let M-X,(w)(R) denote the algebra of the Fourier multipliers on a separable weighted Banach function space X(R, w). We prove that if the Cauchy singular integral operator S is bounded on X( R, w), then M-X,M-w( R) is continuously embedded into L-infinity(R). An important consequence of the continuous embedding M-X,M-w(R) subset of L-infinity(R) is that M-X,M-w(R) is a Banach algebra.
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页码：27 / 36
页数：10
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