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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.00548 |
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| _version_ | 1866916078317207552 |
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| author | Ghara, Soumitra Gupta, Rajeev Reza, Md. Ramiz |
| author_facet | Ghara, Soumitra Gupta, Rajeev Reza, Md. Ramiz |
| contents | For a positive integer $m$ and a finite non-negative Borel measure $μ$ on the unit circle, we study the Hadamard multipliers of higher order weighted Dirichlet-type spaces $\mathcal H_{μ, m}$. We show that if $α>\frac{1}{2},$ then for any $f$ in $\mathcal H_{μ, m},$ the sequence of generalized Ces{à}ro sums $\{σ_n^α[f]\}$ converges to $f$. We further show that if $α=\frac{1}{2}$ then for the Dirac delta measure supported at any point on the unit circle, the previous statement breaks down for every positive integer $m$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00548 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cesàro summability of Taylor series in higher order weighted Dirichlet type spaces Ghara, Soumitra Gupta, Rajeev Reza, Md. Ramiz Functional Analysis 41A10, 40G05, 46E20 For a positive integer $m$ and a finite non-negative Borel measure $μ$ on the unit circle, we study the Hadamard multipliers of higher order weighted Dirichlet-type spaces $\mathcal H_{μ, m}$. We show that if $α>\frac{1}{2},$ then for any $f$ in $\mathcal H_{μ, m},$ the sequence of generalized Ces{à}ro sums $\{σ_n^α[f]\}$ converges to $f$. We further show that if $α=\frac{1}{2}$ then for the Dirac delta measure supported at any point on the unit circle, the previous statement breaks down for every positive integer $m$. |
| title | Cesàro summability of Taylor series in higher order weighted Dirichlet type spaces |
| topic | Functional Analysis 41A10, 40G05, 46E20 |
| url | https://arxiv.org/abs/2401.00548 |