On the non-tangential convergence of Poisson and modified Poisson semigroups at the smoothness points of Lp -functions

BAYRAKÇI DOĞAN, SİMTEN; Shafiev, M.; Aliev, İLHAM

doi:10.1007/s10998-019-00310-4

On the non-tangential convergence of Poisson and modified Poisson semigroups at the smoothness points of Lp -functions

BAYRAKÇI DOĞAN S., Shafiev M. F., Aliev I. A.

Periodica Mathematica Hungarica, vol.80, no.2, pp.249-258, 2020 (SCI-Expanded, Scopus)

Publication Type: Article / Article
Volume: 80 Issue: 2
Publication Date: 2020
Doi Number: 10.1007/s10998-019-00310-4
Journal Name: Periodica Mathematica Hungarica
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
Page Numbers: pp.249-258
Keywords: Poisson semigroup, Metaharmonic semigroup, Non-tangential convergence, Smoothness point, Rate of convergence
Akdeniz University Affiliated: Yes

Abstract

© 2020, Akadémiai Kiadó, Budapest, Hungary.The high-dimensional version of Fatou’s classical theorem asserts that the Poisson semigroup of a function f∈Lp(Rn),1≤p≤∞, 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 μ-smoothness points of f.