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Boundary behavior of Hardy spaces on angular domains

  • Zhihong WenEmail author
  • Guantie Deng
Original Paper
  • 2 Downloads

Abstract

The aim of this paper is to characterize the behavior of boundary limits of functions in Hardy space on angular domains. We investigate that the Cauchy integral of a function \(f\in L^{p}(\partial D_a)\) is in \(H^{p}(D_a).\) We also prove that the functions in \(H^{p}(D_a)\) are the Cauchy integral of their non-tangential boundary limits. In addition, we establish the orthogonality of non-tangential boundary limits of functions in \(H^{p}(D_a)\) and \(H^{q}(D_a)\).

Keywords

Hardy space Cauchy integral Angular domain Holomorphic 

Mathematics Subject Classification

30H10 30E25 30E20 

Notes

Acknowledgements

The author is grateful to the anonymous referees and the associated editors for their valuable suggestions and insightful comments, which improve the presentation of this paper. This work was carried out when the author was visiting the Department of Mathematics, University of Pittsburgh. The author would like to thank the hospitality of Professor Ming Chen and Professor Dehua Wang. This work was supported by the National Natural Science Foundation of China (no. 11901251), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (no. 17KJD110002) and the Foundation Project of Jiangsu Normal University (no. 16XLR033).

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Copyright information

© Tusi Mathematical Research Group (TMRG) 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsJiangsu Normal UniversityXuzhouPeople’s Republic of China
  2. 2.School of Mathematical SciencesBeijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of EducationBeijingPeople’s Republic of China

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