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Algebras of functions with Fourier coefficients in weighted Orlicz sequence spaces

Alexei Yu. Karlovich
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Abstract

We prove that the set of all integrable functions whose sequences of negative (resp. nonnegative) Fourier coefficients belong to $\ell^1\cap\ell^Φ_{ϕ,w}$ (resp. to $\ell^1\cap\ell^Ψ_{ψ,\varrho}$), where $\ell^Φ_{ϕ,w}$ and $\ell^Ψ_{ψ,\varrho}$ are two-weighted Orlicz sequence spaces, forms an algebra under pointwise multiplication whenever the weight sequences \[ ϕ=\{ϕ_n\},\quad ψ=\{ψ_n\},\quad w=\{w_n\},\quad \varrho=\{\varrho_n\} \] increase and satisfy the $Δ_2$-condition.

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BibTeXRIS

Alexei Yu. Karlovich. 2003-05-07. Algebras of functions with Fourier coefficients in weighted Orlicz sequence spaces. https://arxiv.org/abs/math/0305109

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