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arXiv · 2604.25442

Quantitative estimates for the absolute convergence of wavelet-type series

Grigori A. Karagulyan·Gor A. Melkumyan
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Abstract

We establish new quantitative estimates for general systems of functions with wavelet-type dyadic structure. These estimates are applied to obtain the optimal growth of various types of Weyl multipliers for certain wavelet-type systems. Some of our results are sufficiently general to allow the orthogonality assumption to be removed. In particular, as a consequence of these estimates we show that the condition \begin{equation*} \sum_{n=1}^\infty\frac{1}{nw(n)}<\infty \end{equation*} is necessary and sufficient for an increasing sequence $w(n)$ to be an almost everywhere unconditional convergence Weyl multiplier for an arbitrary wavelet-type system. We also prove that $\log n$ is an almost everywhere convergence Weyl multiplier for any rearranged wavelet-type system, and that this bound is optimal.

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Grigori A. Karagulyan, Gor A. Melkumyan. 2026-04-28. Quantitative estimates for the absolute convergence of wavelet-type series. https://arxiv.org/abs/2604.25442

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