TY  - JOUR
ID  - Ghara2024
LB  - Ghara2024
AU  - Ghara, Soumitra
AU  - Gupta, Rajeev
AU  - Reza, Md. Ramiz
TI  - Cesàro summability of Taylor series in higher order weighted Dirichlet-type spaces
ST  - Cesàro summability of Taylor series in higher order weighted Dirichlet-type spaces
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2024
VL  - 44
IS  - 3
SP  - 373
EP  - 390
DO  - https://doi.org/10.7494/OpMath.2024.44.3.373
UR  - https://doi.org/10.7494/OpMath.2024.44.3.373
AB  - 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 \(m\).
KW  - weighted Dirichlet-type integrals
KW  - Cesàro mean
KW  - summability
KW  - Hadamard multiplication
SN  - 1232-9274
ER  -