Banach algebra of the Fourier multipliers on weighted Banach function spaces

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7 Citations (Scopus)

Abstract

Let MX,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), thenMX,w(ℝ) is continuously embedded into L∞(ℝ). An important consequence of the continuous embedding MX,w(ℝ) ⊂ L∞(ℝ) is that MX,w(ℝ) is a Banach algebra.

Original languageEnglish
Pages (from-to)27-36
Number of pages10
JournalConcrete Operators
Volume2
Issue number1
DOIs
Publication statusPublished - 10 Mar 2015

Keywords

  • Banach function space
  • Cauchy singular integral operator
  • Fourier convolution operator
  • Fourier multiplier
  • Muckenhoupt-type weight
  • rearrangement-invariant space
  • variable Lebesgue space

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