Hausdorff operators in hardy spaces on cartan type domains in Cn

L. Aizenberg, E. Liflyand, A. Vidras

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

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Abstract

The main results of the present paper are two-fold. Firstly, they describe a broad class of bounded domains D ⊂ Cn allowing to decide, by elementary inductive means, whether a holomorphic function f in D belongs to the corresponding Hardy space Hp (D), p > 0. Secondly, based on previous results, we define for such domains the corresponding Hausdorff operators and formulate sufficient conditions for such operators to be bounded. Similar results are also given for Bergman spaces.

Original languageEnglish
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages27-46
Number of pages20
DOIs
StatePublished - 2016

Publication series

NameContemporary Mathematics
Volume667
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Bibliographical note

Publisher Copyright:
© 2016 L. Aizenberg, E. Liflyand, A. Vidras.

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