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On the non-tangential convergence of Poisson and modified Poisson semigroups at the smoothness points of \(L_{p}\)-functions

  • Simten BayrakciEmail author
  • M. F. Shafiev
  • Ilham A. Aliev
Article
  • 16 Downloads

Abstract

The high-dimensional version of Fatou’s classical theorem asserts that the Poisson semigroup of a function \(f\in L_{p}(\mathbb {R}^{n}), \ 1\le p \le \infty \), converges to f non-tangentially at Lebesque points. In this paper we investigate the rate of non-tangential convergence of Poisson and metaharmonic semigroups at \(\mu \)-smoothness points of f.

Keywords

Poisson semigroup Metaharmonic semigroup Non-tangential convergence Smoothness point Rate of convergence 

Mathematics Subject Classification

31A05 31A20 35J05 42B99 

Notes

Acknowledgements

The authors would like to thank the editor and the anonymous referees for their carefully reading the manuscript and useful comments and suggestions, which improved this paper.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2020

Authors and Affiliations

  • Simten Bayrakci
    • 1
    Email author
  • M. F. Shafiev
    • 2
  • Ilham A. Aliev
    • 1
  1. 1.Department of MathematicsAkdeniz UniversityAntalyaTurkey
  2. 2.Azerbaijan National Aviation AcademyBakuAzerbaijan

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