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Embedding Theorems for Dirichlet Type Spaces

  • Songxiao Li (a1), Junming Liu (a2) and Cheng Yuan (a2)

Abstract

We use the Carleson measure-embedding theorem for weighted Bergman spaces to characterize the positive Borel measures $\unicode[STIX]{x1D707}$ on the unit disc such that certain analytic function spaces of Dirichlet type are embedded (compactly embedded) in certain tent spaces associated with a measure  $\unicode[STIX]{x1D707}$ . We apply these results to study Volterra operators and multipliers acting on the mentioned spaces of Dirichlet type.

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J. Liu is the corresponding author. This work was supported by NNSF of China (Grant No. 11801094 and No.11720101003).

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Embedding Theorems for Dirichlet Type Spaces

  • Songxiao Li (a1), Junming Liu (a2) and Cheng Yuan (a2)

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