Generalized localization for spherical partial sums of multiple Fourier series

DOI10.1134/S1064562419060012zbMath1446.42002OpenAlexW2909995276MaRDI QIDQ5918887

Ravshan Ashurov

Publication date: 24 June 2020

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562419060012

zbMATH Keywords

multiple Fourier seriesprinciple of localizationspherical sums

Mathematics Subject Classification ID

Convergence and absolute convergence of Fourier and trigonometric series (42A20) Summability and absolute summability of Fourier and trigonometric series (42A24)

Cites Work

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• Almost-everywhere convergence of Fourier integrals for functions in Sobolev spaces, and an \(L^ 2\)-localisation principle
• The generalized localization for multiple Fourier integrals
• Regularity and integrability of spherical means
• Generalized localization of Fourier series with respect to the eigenfunctions of the Laplace operator in the classes \(L_ p\)
• Radial weights and mixed norm inequalities for the disc multiplier
• Pointwise Fourier inversion and localisation in \(\mathbb{R}^n\)
• Almost Everywhere Summability of Fourier Integrals

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