On wavelet polynomials and Weyl multipliers
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866909948340862976 |
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| author | Kamont, Anna Karagulyan, Grigori A. |
| author_facet | Kamont, Anna Karagulyan, Grigori A. |
| contents | For the wavelet type orthonormal systems $ϕ_n$, we establish a new bound
\begin{equation}
\left\|\max_{1\le m\le n}\left|\sum_{j\in G_m}\langle f,ϕ_j\rangle ϕ_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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_03124 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On wavelet polynomials and Weyl multipliers Kamont, Anna Karagulyan, Grigori A. Classical Analysis and ODEs 42C05, 42C10, 42C20, 42C40 For the wavelet type orthonormal systems $ϕ_n$, we establish a new bound \begin{equation} \left\|\max_{1\le m\le n}\left|\sum_{j\in G_m}\langle f,ϕ_j\rangle ϕ_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. |
| title | On wavelet polynomials and Weyl multipliers |
| topic | Classical Analysis and ODEs 42C05, 42C10, 42C20, 42C40 |
| url | https://arxiv.org/abs/2104.03124 |