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arXiv · 2104.03124

On wavelet polynomials and Weyl multipliers

Anna Kamont·Grigori A. Karagulyan
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Abstract

For the wavelet type orthonormal systems $\phi_n$, we establish a new bound \begin{equation} \left\|\max_{1\le m\le n}\left|\sum_{j\in G_m}\langle f,\phi_j\rangle \phi_j\right|\right\|_p\lesssim \sqrt{\log (n+1)}\cdot \|f\|_p,\quad 1<p<\infty, \end{equation} where $G_m\subset N$ are arbitrary sets of indexes. Using this estimate, we prove that $\log n$ is an almost everywhere convergence Weyl multiplier for any orthonormal system of non-overlapping wavelet polynomials. It will also be remarked that $\log n$ is the optimal sequence in this context.

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Anna Kamont, Grigori A. Karagulyan. 2021-04-07. On wavelet polynomials and Weyl multipliers. https://doi.org/10.1007/s11854-023-0281-4

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