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A CLASS OF SYMBOLS THAT INDUCE BOUNDED COMPOSITION OPERATORS FOR DIRICHLET-TYPE SPACES ON THE DISC

Part of: Holomorphic functions of several complex variables Spaces and algebras of analytic functions

Published online by Cambridge University Press:  14 March 2024

ATHANASIOS BESLIKAS Open the ORCID record for ATHANASIOS BESLIKAS [Opens in a new window]
ATHANASIOS BESLIKAS*
Affiliation:
Doctoral School of Exact and Natural Studies, Institute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, PL30348 Cracow, Poland
*
e-mail: athanasios.beslikas@doctoral.uj.edu.pl
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Abstract

We study the problem of determining the holomorphic self maps of the unit disc that induce a bounded composition operator on Dirichlet-type spaces. We find a class of symbols $\varphi $ that induce a bounded composition operator on the Dirichlet-type spaces, by applying results of the multidimensional theory of composition operators for the weighted Bergman spaces of the bi-disc.

Keywords

Dirichlet-type spacescomposition operatorsweighted Bergman spaces

MSC classification

Primary: 30H99: None of the above, but in this section
Secondary: 30H20: Bergman spaces, Fock spaces 32A25: Integral representations; canonical kernels (Szegő, Bergman, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 6
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The author was supported by the NCN grant SONATA BIS no. 2017/26/E/ST1/00723.

References

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