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arXiv · 2210.11331

Vilenkin-Fourier series in variable Lebesgue spaces

Daviti Adamadze·Tengiz Kopaliani
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Abstract

Let $S_{n}f$ denote the $n$th partial sum of the Vilenkin-Fourier series of a function $f \in L^{1}(G)$. For $1 < p_{-} \leq p_{+} < \infty$, we characterize all exponents $p(\cdot)$ for which the convergence of $S_{n}f$ to $f$ in $L^{p(\cdot)}(G)$ holds whenever $f \in L^{p(\cdot)}(G)$.

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BibTeXRIS

Daviti Adamadze, Tengiz Kopaliani. 2022-10-20. Vilenkin-Fourier series in variable Lebesgue spaces. https://arxiv.org/abs/2210.11331

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