Banach algebra of the Fourier multipliers on weighted Banach function spaces

• Autorzy: Alexei Karlovich
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Concrete Operators
• Rocznik: 2015
• Tom: 2
• Numer: 1

Daty

otrzymano

2015-01-28

zaakceptowano

2015-02-23

online

2015-03-10

Twórcy

autor

Alexei Karlovich

• Centro de Matemática e Aplicações, Departamento de Matemática, Faculdade de
  Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829–516 Caparica, Portugal

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Identyfikatory

DOI

10.1515/conop-2015-0001