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Browsing by Author "Reza, Md. Ramiz"

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    Item type:Article, Access status: Open Access ,
    Cesàro summability of Taylor series in higher order weighted Dirichlet-type spaces
    (Wydawnictwa AGH, 2024) Ghara, Soumitra; Gupta, Rajeev; Reza, Md. Ramiz
    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 $m$.