Hadamard Multipliers on Weighted Dirichlet Spaces
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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.
KeywordsDirichlet space Superharmonic weight Fejér theorem
Mathematics Subject ClassificationPrimary 41A10 Secondary 41A17 40G05 40G10
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