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

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Abstract

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).

Original languageEnglish
Number of pages16
JournalJournal of Mathematical Sciences (United States)
DOIs
Publication statusPublished - 10 Oct 2022

Keywords

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

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