@Article{Ghara2024,
author = "Ghara, Soumitra and Gupta, Rajeev and Reza, Md. Ramiz",
title = "Cesàro summability of Taylor series in higher order weighted Dirichlet-type spaces",
journal = "Opuscula Math.",
year = "2024",
volume = "44",
number = "3",
pages = "373--390",
doi = "https://doi.org/10.7494/OpMath.2024.44.3.373",
url = "https://doi.org/10.7494/OpMath.2024.44.3.373",
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 \(\alpha\gt\frac{1}{2}\), then for any \(f\) in \(\mathcal H_{\mu, m}\) the sequence of generalized Cesàro 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 \(m\).",
keywords = "weighted Dirichlet-type integrals, Cesàro mean, summability, Hadamard multiplication",
issn = "1232-9274"
}