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arXiv · 2009.12295

Cesàro summability of Taylor series in weighted Dirichlet spaces

Javad Mashreghi·Pierre-Olivier Parisé·Thomas Ransford
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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 $(C,α)$-summable to the function in the norm of the space, provided that $α>1/2$. We further show that the constant $1/2$ is sharp, in marked contrast with the classical case of the disk algebra.

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Javad Mashreghi, Pierre-Olivier Parisé, Thomas Ransford. 2020-09-25. Cesàro summability of Taylor series in weighted Dirichlet spaces. https://arxiv.org/abs/2009.12295

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