Hausdorff operators in hardy spaces on cartan type domains in Cn

L. Aizenberg; E. Liflyand; A. Vidras

doi:10.1090/conm/667/13529

Hausdorff operators in hardy spaces on cartan type domains in Cⁿ

L. Aizenberg, E. Liflyand, A. Vidras

Department of Mathematics

University of Cyprus

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

7 Scopus citations

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 H^p (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 language	English
Title of host publication	Contemporary Mathematics
Publisher	American Mathematical Society
Pages	27-46
Number of pages	20
DOIs	https://doi.org/10.1090/conm/667/13529
State	Published - 2016

Publication series

Name	Contemporary Mathematics
Volume	667
ISSN (Print)	0271-4132
ISSN (Electronic)	1098-3627

Bibliographical note

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

Access to Document

10.1090/conm/667/13529

Cite this

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