On the non-tangential convergence of Poisson and modified Poisson semigroups at the smoothness points of \(L_p\)-functions

DOI10.1007/S10998-019-00310-4zbMath1463.31009OpenAlexW3000588518MaRDI QIDQ2003770

M. F. Shafiev, Ilham A. Aliev, Simten Bayrakçı

Publication date: 2 October 2020

Published in: Periodica Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10998-019-00310-4

zbMATH Keywords

rate of convergencePoisson semigroupvertexnon-tangential convergencemetaharmonic semigroupFatou's theoremsmoothness point

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Harmonic analysis in several variables (42B99) Boundary behavior of harmonic functions in higher dimensions (31B25) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20)

Related Items (1)

On the convergence of the Abel-Poisson means of multiple Fourier series

Cites Work

• On the Gauss-Weierstrass summability of multiple trigonometric series at \(\mu\)-smoothness points
• On certain maximal functions and approach regions
• Wavelet-like transforms for admissible semi-groups; inversion formulas for potentials and Radon transforms
• On a rate of convergence of truncated hypersingular integrals associated to Riesz and Bessel potentials
• The rate of convergence of truncated hypersingular integrals generated by the Poisson and metaharmonic semigroups
• A counterexample on nontangential convergence for oscillatory integrals
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