\(L^p\)-Regularity for \(\bar{\partial }\) on Products of Unit Balls

Research Paper
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Abstract

In this paper, we prove that the \(\bar{\partial }\)-operator has closed range in \(L^p\)-spaces and further the canonical solution of the \(\bar{\partial }\)-problem gains 1/2 derivative in the so-called partial \(L^p\)-Sobolev spaces as well as global boundary regularity for \(\bar{\partial }\) on products of unit balls.

Keywords

\(\bar{\partial }\)-Problem Closed range Product domain \(L^p\)-Sobolev regularity 

Notes

Acknowledgements

The author thanks the anonymous referees for their careful reading of the paper and valuable remarks and helpful suggestions that improved the presentation of the paper.

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Copyright information

© Shiraz University 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceUniversity of JeddahJeddahSaudi Arabia
  2. 2.Department of Mathematics, Faculty of ScienceBeni-Suef UniversityBeni-SuefEgypt

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