Boundedness of the Bergman Projection and Some Properties of Bergman Type Spaces

Alexey Karapetyants, Humberto Rafeiro, Stefan Samko

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We give a simple proof of the boundedness of Bergman projection in various Banach spaces of functions on the unit disc in the complex plain. The approach of the paper is based on the idea of Zaharyuta and Yudovich (Uspekhi Mat Nauk 19(2):139–142, 1964) where the boundedness of the Bergman projection in Lebesgue spaces was proved using Calderón–Zygmund operators. We exploit this approach and treat the cases of variable exponent Lebesgue space, Orlicz space and variable exponent generalized Morrey spaces. In the case of variable exponent Lebesgue space the boundedness result is known, so in that case we provide a simpler proof, whereas the other cases are new. The major idea of this paper is to show that the approach can be applied to a wide range of function spaces. We also study the rate of growth of functions near the boundary in spaces under consideration and their approximation by mollified dilations.

Original languageEnglish
Pages (from-to)275-289
Number of pages15
JournalComplex Analysis and Operator Theory
Volume13
Issue number1
DOIs
Publication statusPublished - Feb 13 2019
Externally publishedYes

Keywords

  • Bergman projection
  • Bergman space
  • Orlicz space
  • Variable exponent Lebesgue space
  • Variable exponent generalized Morrey space

ASJC Scopus subject areas

  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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