Cesàro summability of Taylor series in weighted Dirichlet spaces

Abstract

We show that, in every weighted Dirichlet space on the unit disk with superharmonic weight, the Taylor series of a function in the space is $(C,\alpha )$-summable to the function in the norm of the space, provided that $\alpha >1/2$. We further show that the constant $1/2$ is sharp, in marked contrast with the classical case of the disk algebra.

7 pages