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arXiv · 2401.00548

Ces\`aro summability of Taylor series in higher order weighted Dirichlet type spaces

Soumitra Ghara·Rajeev Gupta·Md. Ramiz Reza
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Abstract

For a positive integer $m$ and a finite non-negative Borel measure $\mu$ on the unit circle, we study the Hadamard multipliers of higher order weighted Dirichlet-type spaces $\mathcal H_{\mu, m}$. We show that if $\alpha>\frac{1}{2},$ then for any $f$ in $\mathcal H_{\mu, m},$ the sequence of generalized Ces{\`a}ro sums $\{\sigma_n^{\alpha}[f]\}$ converges to $f$. We further show that if $\alpha=\frac{1}{2}$ then for the Dirac delta measure supported at any point on the unit circle, the previous statement breaks down for every positive integer $m$.

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Soumitra Ghara, Rajeev Gupta, Md. Ramiz Reza. 2023-12-31. Ces\`aro summability of Taylor series in higher order weighted Dirichlet type spaces. https://arxiv.org/abs/2401.00548

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