Abstract and Applied Analysis

On Generalized Localization of Fourier Inversion Associated with an Elliptic Operator for Distributions

Ravshan Ashurov, Almaz Butaev, and Biswajeet Pradhan

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Abstract

We study the behavior of Fourier integrals summed by the symbols of elliptic operators and pointwise convergence of Fourier inversion. We consider generalized localization principle which in classical L p spaces was investigated by Sjölin (1983), Carbery and Soria (1988, 1997) and Alimov (1993). Proceeding these studies, in this paper, we establish sharp conditions for generalized localization in the class of finitely supported distributions.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 649848, 13 pages.

Dates
First available in Project Euclid: 5 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365174064

Digital Object Identifier
doi:10.1155/2012/649848

Mathematical Reviews number (MathSciNet)
MR2955035

Zentralblatt MATH identifier
1250.42034

Citation

Ashurov, Ravshan; Butaev, Almaz; Pradhan, Biswajeet. On Generalized Localization of Fourier Inversion Associated with an Elliptic Operator for Distributions. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 649848, 13 pages. doi:10.1155/2012/649848. https://projecteuclid.org/euclid.aaa/1365174064


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