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On mixed norm Bergman–Orlicz–Morrey spaces

  • Alexey N. Karapetyants EMAIL logo and Stefan G. Samko

Abstract

Following the ideas of our previous research, in this paper we continue the study of new Bergman-type spaces on the unit disc with mixed norm in terms of Fourier coefficients. Here we deal with the case where the sequence of norms of Fourier coefficients in the Orlicz–Morrey space in radial variable belongs to lq. We study the boundedness of the Bergman projection and provide a description of functions in these spaces via the behavior of their Taylor coefficients.

MSC 2010: 30H20; 46E30; 46E15

Dedicated to Academician Vakhtang Kokilashvili on the occasion of his 80th birthday


Award Identifier / Grant number: 18-01-00094

Award Identifier / Grant number: 18-51-05009 Apm_a

Funding statement: The authors are partially supported by the grant 18-01-00094 of Russian Foundation of Basic Research. The first author is also partially supported by the grant 18-51-05009 Apm_a of Russian Foundation of Basic Research.

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Received: 2017-8-3
Revised: 2018-1-6
Accepted: 2018-1-8
Published Online: 2018-5-9
Published in Print: 2018-6-1

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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