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arXiv · 2601.20685

Divergent Fourier Series with Respect to Biorthonormal Systems in Function Spaces Near $L^1$

Nikoloz Devdariani
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Abstract

In this paper, we generalize Bochkarev's theorem, which states that for any uniformly bounded biorthonormal system $\Phi$, there exists a Lebesgue integrable function whose Fourier series with respect to the system $\Phi$ diverges on a set of positive measure. We find the class of variable exponent Lebesgue spaces $L^{p(\cdot)}([0,1]^n)$, where $1 < p(x) < \infty$ almost everywhere on $[0,1]^n$, such that the aforementioned Bochkarev's theorem holds.

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BibTeXRIS

Nikoloz Devdariani. 2026-01-28. Divergent Fourier Series with Respect to Biorthonormal Systems in Function Spaces Near $L^1$. https://arxiv.org/abs/2601.20685

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