Fourier representations in Bergman spaces

Debraj Chakrabarti, Pranav Upadrashta

Research output: Contribution to journalArticlepeer-review


We consider a class of domains, generalizing the upper half-plane, and admitting rotational, translational and scaling symmetries analogous to the half-plane. We prove Paley-Wiener type representations of functions in Bergman spaces of such domains with respect to each of these three groups of symmetries. The Fourier series, Fourier integral and Mellin integral representations so obtained may be used to give representations of the Bergman kernels of these domains.

Original languageEnglish
Pages (from-to)464-489
Number of pages26
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - Jul 1 2019


  • Bedford-Pinchuk eggs
  • Bergman space
  • Holomorphic Fourier transforms
  • Paley-Wiener representations


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