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Berezin symbols and some problems on the Dirichlet space

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  • Ulaş Yamancı

    (Suleyman Demirel University)

Abstract

In this article, we characterize the classes $$S_{p}^{w}$$ S p w classes in terms of the boundary behavior of Berezin symbols of the weighted shift operators on the Dirichlet space $${\mathcal {D}}\left( {\mathbb {D}}\right) $$ D D . Also, we give a result related with the asymptotic multiplicative property of the Berezin symbol of any operator on reproducing kernel Hilbert space. Moreover, by using Berezin symbols, we give some condition for st- $$\left( DL\right) $$ D L convergence of a series of complex numbers.

Suggested Citation

  • Ulaş Yamancı, 2025. "Berezin symbols and some problems on the Dirichlet space," Indian Journal of Pure and Applied Mathematics, Springer, vol. 56(3), pages 1269-1277, September.
    • Handle: RePEc:spr:indpam:v:56:y:2025:i:3:d:10.1007_s13226-024-00553-z
    DOI: 10.1007/s13226-024-00553-z
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