INVERTIBILITY OF FOURIER CONVOLUTION OPERATORS WITH PIECEWISE CONTINUOUS SYMBOLS ON BANACH FUNCTION SPACES

被引：0

作者：

Fernandes, Claudio ^{[1
,2
]}

Karlovich, Alexei ^{[1
,2
]}

Valente, Marcio ^{[2
]}

机构：

[1] Univ Nova Lisboa, Fac Ciencias & Tecnol, Ctr Matemat & Aplicaoes CMA, P-2829516 Quinta Da Torre, Caparica, Portugal

[2] Univ Nova Lisboa, Fac Ciencias & Tecnol, Dept Matemat, P-2829516 Quinta Da Torre, Caparica, Portugal

来源：

TRANSACTIONS OF A RAZMADZE MATHEMATICAL INSTITUTE | 2021年 / 175卷 / 01期

关键词：

Fourier convolution operator; Fourier multiplier; Piecwise constant function; Piecewise continuous function; Invertibility;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We extend results on the invertibility of Fourier convolution operators with piecewise continuous symbols on the Lebesgue space L-p (R), p is an element of (1, infinity), obtained by Roland Duduchava in the late 1970s, to the setting of a separable Banach function space X(R) such that the Hardy-Littlewood maximal operator is bounded on X(R) and on its associate space X'(R). We specify our results in the case of rearrangement-invariant spaces with suitable Muckenhoupt weights.

引用

页码：49 / 61

页数：13

共 12 条

[1] INVERTIBILITY OF FOURIER CONVOLUTION OPERATORS WITH PC SYMBOLS ON VARIABLE LEBESGUE SPACES WITH KHVEDELIDZE WEIGHTS
Fernandes C.
Karlovych O.
Medalha S.
Journal of Mathematical Sciences, 2022, 266 (3) : 419 - 434
[2] NONCOMPACTNESS OF FOURIER CONVOLUTION OPERATORS ON BANACH FUNCTION SPACES
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[5] COMMUTATORS OF CONVOLUTION TYPE OPERATORS ON SOME BANACH FUNCTION SPACES
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[6] Banach algebra of the Fourier multipliers on weighted Banach function spaces
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[7] INVERTIBLE COMPOSITION OPERATORS ON BANACH FUNCTION SPACES
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[8] Finite Section Method for a Banach Algebra of Convolution Type Operators on Lp(R) with Symbols Generated by PC and SO
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[9] A SEMI-FREDHOLM THEORY FOR WIENER-HOPF-HANKEL OPERATORS WITH PIECEWISE ALMOST PERIODIC FOURIER SYMBOLS
Castro, L. P.
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JOURNAL OF OPERATOR THEORY, 2009, 62 (01) : 3 - 31
[10] A Fourier multiplier theorem on anisotropic Hardy spaces associated with ball quasi-Banach function spaces
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ANNALS OF FUNCTIONAL ANALYSIS, 2025, 16 (01)

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