INVERTIBILITY OF FOURIER CONVOLUTION OPERATORS WITH PC SYMBOLS ON VARIABLE LEBESGUE SPACES WITH KHVEDELIDZE WEIGHTS

被引：0

作者：

Fernandes C. ^{[1
,2
]}

Karlovych O. ^{[1
,2
]}

Medalha S. ^{[2
]}

机构：

[1] Centro de Matemática e Aplicações (CMA), Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, Caparica

[2] Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, Caparica

来源：

Journal of Mathematical Sciences | 2022年 / 266卷 / 3期

关键词：

Fourier convolution operator; Fourier multiplier; Invertibility; Khvedelidze weight; Piecewise continuous function; Variable Lebesgue space;

D O I：

10.1007/s10958-022-05897-7

中图分类号：

学科分类号：

摘要：

Let p(·) : R→ (1 , ∞) be a sufficiently regular variable exponent and ϱ be a Khvedelidze weight on R. Suppose that a function a belongs to the algebra PCp(·),ϱ of piecewise continuous Fourier multipliers on the weighted variable Lebesgue space Lp(·)(R, ϱ). We show that the Fourier convolution operator W(a) = F- 1aF is invertible on the space Lp(·)(R, ϱ) if and only if its symbol a is invertible in L∞(R). © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

引用

页码：419 / 434

页数：15

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