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Hadamard Multipliers on Weighted Dirichlet Spaces

  • Javad Mashreghi
  • Thomas RansfordEmail author
Article
  • 34 Downloads

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.

Keywords

Dirichlet space Superharmonic weight Fejér theorem 

Mathematics Subject Classification

Primary 41A10 Secondary 41A17 40G05 40G10 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Département de mathématiques et de statistiqueUniversité LavalQuébecCanada

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