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

The high-dimensional version of Fatou’s classical theorem asserts that the Poisson semigroup of a function f ∈ L p ( R n ) , 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...

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Bibliographic Details
Published in:Periodica mathematica Hungarica 2020, Vol.80 (2), p.249-258
Main Authors: Bayrakci, Simten, Shafiev, M. F., Aliev, Ilham A.
Format: Article
Language:English
Subjects:
Convergence
Mathematics
Mathematics and Statistics
Smoothness
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Summary:The high-dimensional version of Fatou’s classical theorem asserts that the Poisson semigroup of a function f ∈ L p ( R n ) , 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 .
ISSN:0031-5303
1588-2829
DOI:10.1007/s10998-019-00310-4