Algebras of functions with Fourier coefficients in weighted Orlicz sequence spaces

Details Algebras of functions with Fourier coefficients in weighted Orlicz sequence spaces Algebras of functions with Fourier coefficients in weighted Orlicz sequence spaces

2003-05-07

arxiv.org/abs/math/0305109v1

Mathematics

Functional Analysis

Scientific paper

We prove that the set of all integrable functions whose sequences of negative (resp. nonnegative) Fourier coefficients belong to $\ell^1\cap\ell^\Phi_{\phi,w}$ (resp. to $\ell^1\cap\ell^\Psi_{\psi,\varrho}$), where $\ell^\Phi_{\phi,w}$ and $\ell^\Psi_{\psi,\varrho}$ are two-weighted Orlicz sequence spaces, forms an algebra under pointwise multiplication whenever the weight sequences \[ \phi=\{\phi_n\},\quad \psi=\{\psi_n\},\quad w=\{w_n\},\quad \varrho=\{\varrho_n\} \] increase and satisfy the $\Delta_2$-condition.

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