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Banach algebras of Fourier multipliers equivalent at infinity to nice Fourier multipliers
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Orientador(es)
Resumo(s)
Let MX(R) be the Banach algebra of all Fourier multipliers on a Banach function space X(R) such that the Hardy–Littlewood maximal operator is bounded on X(R) and on its associate space X′(R). For two sets Ψ, Ω⊂ MX(R), let ΨΩ be the set of those c∈ Ψ for which there exists d∈ Ω such that the multiplier norm of χR\[-N,N](c- d) tends to zero as N→ ∞. In this case, we say that the Fourier multiplier c is equivalent at infinity to the Fourier multiplier d. We show that if Ω is a unital Banach subalgebra of MX(R) consisting of nice Fourier multipliers (for instance, continuous or slowly oscillating in certain sense) and Ψ is an arbitrary unital Banach subalgebra of MX(R), then ΨΩ is a also a unital Banach subalgebra of MX(R).
Descrição
This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UIDB/MAT/00297/2020 (Centro de Matematica e Aplicacoes) and by the SEP-CONACYT project A1-S-8793 (Mexico).
Palavras-chave
Banach algebra C-algebra Equivalence at infinity Fourier convolution operator Fourier multiplier Slowly oscillating function Analysis Algebra and Number Theory