Duality and Reproducing Kernels for Dirichlet-Type Spaces

Authors

  • Effie A. Oyugi Department of Pure and Applied Mathematics, Maseno University, Maseno, Kenya
  • Job O. Bonyo Department of Mathematics, Multimedia University of Kenya, Nairobi, Kenya.
  • John O. Agure Department of Pure and Applied Mathematics, Maseno University, Maseno, Kenya

DOI:

https://doi.org/10.56947/amcs.v36.937

Keywords:

Dirichlet-type spaces, weighted Bergman spaces, differentiation operator, isometric isomorphism, duality, reproducing kernels

Abstract

Using an isometric differentiation isomorphism between the weighted Dirichlet-type spaces and the weighted Bergman space, we determine the duals of the weighted Dirichlet-type spaces of the unit disk and the upper half-plane. Further, we compute the reproducing kernels for the Hilbert version of these spaces.

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Published

2026-09-20

Issue

Vol. 36 (2026)

Section

Mathematics

License

Copyright (c) 2026 Annals of Mathematics and Computer Science

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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