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The principle of general localization on unit sphere

In this paper we study the general localization principle for Fourier–Laplace series on unit sphere SN⊂RN+1. Weak type (1,1) property of maximal functions is used to establish the estimates of the maximal operators of Riesz means at critical index. The properties Jacobi polynomials are used in estim...

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Main Author: Ahmedov, Anvarjon
Format: Article
Language:English
Published: Elsevier 2009
Online Access:http://psasir.upm.edu.my/id/eprint/17280/1/The%20principle%20of%20general%20localization%20on%20unit%20sphere.pdf
http://psasir.upm.edu.my/id/eprint/17280/
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spelling my.upm.eprints.172802017-04-19T01:33:15Z http://psasir.upm.edu.my/id/eprint/17280/ The principle of general localization on unit sphere Ahmedov, Anvarjon In this paper we study the general localization principle for Fourier–Laplace series on unit sphere SN⊂RN+1. Weak type (1,1) property of maximal functions is used to establish the estimates of the maximal operators of Riesz means at critical index. The properties Jacobi polynomials are used in estimating the maximal operators of spectral expansions in L2(SN). For extending positive results on critical line, 1⩽p⩽2, we apply interpolation theorem for the family of the linear operators of weak types. The generalized localization principle is established by the analysis of spectral expansions in L2. We have proved the sufficient conditions for the almost everywhere convergence of Fourier–Laplace series by Riesz means on the critical line. Elsevier 2009-08 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/17280/1/The%20principle%20of%20general%20localization%20on%20unit%20sphere.pdf Ahmedov, Anvarjon (2009) The principle of general localization on unit sphere. Journal of Mathematical Analysis and Applications, 356 (1). pp. 310-321. ISSN 0022-247X; ESSN: 1096-0813 10.1016/j.jmaa.2009.03.019
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description In this paper we study the general localization principle for Fourier–Laplace series on unit sphere SN⊂RN+1. Weak type (1,1) property of maximal functions is used to establish the estimates of the maximal operators of Riesz means at critical index. The properties Jacobi polynomials are used in estimating the maximal operators of spectral expansions in L2(SN). For extending positive results on critical line, 1⩽p⩽2, we apply interpolation theorem for the family of the linear operators of weak types. The generalized localization principle is established by the analysis of spectral expansions in L2. We have proved the sufficient conditions for the almost everywhere convergence of Fourier–Laplace series by Riesz means on the critical line.
format Article
author Ahmedov, Anvarjon
spellingShingle Ahmedov, Anvarjon
The principle of general localization on unit sphere
author_facet Ahmedov, Anvarjon
author_sort Ahmedov, Anvarjon
title The principle of general localization on unit sphere
title_short The principle of general localization on unit sphere
title_full The principle of general localization on unit sphere
title_fullStr The principle of general localization on unit sphere
title_full_unstemmed The principle of general localization on unit sphere
title_sort principle of general localization on unit sphere
publisher Elsevier
publishDate 2009
url http://psasir.upm.edu.my/id/eprint/17280/1/The%20principle%20of%20general%20localization%20on%20unit%20sphere.pdf
http://psasir.upm.edu.my/id/eprint/17280/
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score 13.211869

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