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Banach algebra of the Fourier multipliers on weighted Banach function spaces

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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.
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
otrzymano
2015-01-28
zaakceptowano
2015-02-23
online
2015-03-10
Twórcy
  • Centro de Matemática e Aplicações, Departamento de Matemática, Faculdade de
    Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829–516 Caparica, Portugal, Sergey.M.Zagorodnyuk@univer.kharkov.ua
Bibliografia
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  • [5] Böttcher A., Karlovich Yu.I., Spitkovsky I.M., Convolution Operators and Factorization of Almost Periodic Matrix Functions.Operator Theory: Advances and Applications, 131. Birkhäuser, Basel, 2002. DOI: 10.1007/978-3-0348-8152-4[Crossref]
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  • [7] Cruz-Uribe D., Diening L., Hästö P., Themaximal operator on weighted variable Lebesgue spaces. Frac. Calc. Appl. Anal., 14,2011, 361–374. DOI: 10.2478/s13540-011-0023-7[Crossref]
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  • [13] Fremlin D.H., Measure Theory. Vol. 2: Broad Foundations, Torres Fremlin, Colchester, 2003.
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  • [17] Karlovich A.Yu., Algebras of singular integral operators with PC coefficients in rearrangement-invariant spaces with Muckenhouptweights. J. Oper. Theory, 2002, 47, 303–323.
  • [18] Karlovich A.Yu., Spitkovsky I.M., The Cauchy singular integral operator on weighted variable Lebesgue spaces. In ConcreteOperators, Spectral Theory, Operators in Harmonic Analysis and Approximation, Birkhäuser, Basel. Operator Theory: Advancesand Applications, 2014, 236, pp. 275–291. DOI: 10.1007/978 − 3 − 0348 − 0648 − 017[Crossref]
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_conop-2015-0001
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