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Hadamard Multipliers on Weighted Dirichlet Spaces

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Abstract

The Hadamard product of two power series is obtained by multiplying them coefficientwise. In this paper we characterize those power series that act as Hadamard multipliers on all weighted Dirichlet spaces on the disk with superharmonic weights, and we obtain sharp estimates on the corresponding multiplier norms. Applications include an analogue of Fejér’s theorem in these spaces, and a new estimate for the weighted Dirichlet integrals of dilates.

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Authors and Affiliations

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

    Javad Mashreghi & Thomas Ransford

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  1. Javad Mashreghi
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  2. Thomas Ransford
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Correspondence to Thomas Ransford.

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JM supported by an NSERC grant. TR supported by grants from NSERC and the Canada Research Chairs program.

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Mashreghi, J., Ransford, T. Hadamard Multipliers on Weighted Dirichlet Spaces. Integr. Equ. Oper. Theory 91, 52 (2019). https://doi.org/10.1007/s00020-019-2551-1

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  • DOI: https://doi.org/10.1007/s00020-019-2551-1

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