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.
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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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Bayrakci, S., Shafiev, M.F. & Aliev, I.A. On the non-tangential convergence of Poisson and modified Poisson semigroups at the smoothness points of \(L_{p}\)-functions. Period Math Hung 80, 249–258 (2020). https://doi.org/10.1007/s10998-019-00310-4
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DOI: https://doi.org/10.1007/s10998-019-00310-4
Keywords
- Poisson semigroup
- Metaharmonic semigroup
- Non-tangential convergence
- Smoothness point
- Rate of convergence