Banach algebra of the Fourier multipliers on weighted Banach function spaces

Alexei Karlovich

Concrete Operators (2015)

  • Volume: 2, Issue: 1, page 27-36, electronic only
  • ISSN: 2299-3282

Abstract

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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.

How to cite

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Alexei Karlovich. "Banach algebra of the Fourier multipliers on weighted Banach function spaces." Concrete Operators 2.1 (2015): 27-36, electronic only. <http://eudml.org/doc/269960>.

@article{AlexeiKarlovich2015,
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.},
author = {Alexei Karlovich},
journal = {Concrete Operators},
keywords = {Fourier convolution operator; Fourier multiplier; Banach function space; Cauchy singular integral operator; rearrangement-invariant space; variable Lebesgue space; Muckenhoupt-type weight; Cauchy singular integral operator; rearrangement invariant space},
language = {eng},
number = {1},
pages = {27-36, electronic only},
title = {Banach algebra of the Fourier multipliers on weighted Banach function spaces},
url = {http://eudml.org/doc/269960},
volume = {2},
year = {2015},
}

TY - JOUR
AU - Alexei Karlovich
TI - Banach algebra of the Fourier multipliers on weighted Banach function spaces
JO - Concrete Operators
PY - 2015
VL - 2
IS - 1
SP - 27
EP - 36, electronic only
AB - 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.
LA - eng
KW - Fourier convolution operator; Fourier multiplier; Banach function space; Cauchy singular integral operator; rearrangement-invariant space; variable Lebesgue space; Muckenhoupt-type weight; Cauchy singular integral operator; rearrangement invariant space
UR - http://eudml.org/doc/269960
ER -

References

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