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Cesàro Summability of Taylor Series in Weighted Dirichlet Spaces

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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 \((C,\alpha )\)-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.

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Funding

JM supported by an NSERC Discovery Grant. POP supported by an NSERC Alexander-Graham-Bell Scholarship. TR supported by grants from NSERC and the Canada Research Chairs program.

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Authors and Affiliations

  1. Département de mathématiques et de statistique, Université Laval, Québec City, G1V 0A6, Canada

    Javad Mashreghi, Pierre-Olivier Parisé & Thomas Ransford

Authors
  1. Javad Mashreghi
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  2. Pierre-Olivier Parisé
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  3. Thomas Ransford
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Correspondence to Thomas Ransford.

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Communicated by Dan Volok.

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JM supported by an NSERC Discovery Grant. POP supported by an NSERC Alexander-Graham-Bell Scholarship. TR supported by grants from NSERC and the Canada Research Chairs program.

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Mashreghi, J., Parisé, PO. & Ransford, T. Cesàro Summability of Taylor Series in Weighted Dirichlet Spaces. Complex Anal. Oper. Theory 15, 7 (2021). https://doi.org/10.1007/s11785-020-01058-3

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  • DOI: https://doi.org/10.1007/s11785-020-01058-3

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