The estimations for maximal operators

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• 作者：Anvarjon Ahmedov^a ; ^{anvar@eng.upm.edu.my}
• 关键词：Maximal operators ; Fourier– ; Laplace series ; Riesz means ; Spectral function ; Laplace– ; Beltrami operator
• 刊名：Applied Mathematics Letters
• 出版年：2011
• 出版时间：May 2011
• 年：2011
• 卷：24
• 期：5
• 页码：615-619
• 全文大小：210 K

文摘

In this paper we study the almost everywhere convergence of the spectral expansions related to the Laplace–Beltrami operator on the unit sphere. Using the spectral properties of the functions with logarithmic singularities, the estimate for maximal operator of the Riesz means of the partial sums of the Fourier–Laplace series is established. We have constructed a different method for investigating the summability problems of Fourier–Laplace series, which based on the theory of spectral decompositions of the self-adjoint Laplace–Beltrami operator.