Paper detail

Cesàro summability of Taylor series in higher order weighted Dirichlet type spaces

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 $m$.