Article

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

Ravshan AshurovInstitute of Mathematics, National University of Uzbekistan, Hodjaeva Street 29, Tashkent 100125, UzbekistanAlmaz ButaevDepartment of Civil Engineering, Faculty of Engineering, Geospatial, Information Science Center (GIS RC), University Putra Malaysia (UPM), 43400 Serdang, Selangor, MalaysiaBiswajeet PradhanDepartment of Civil Engineering, Faculty of Engineering, Geospatial, Information Science Center (GIS RC), University Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia

Abstract and Applied Analysisjournal2012en

ABI

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.

Topics

Advanced Harmonic Analysis Research Advanced Banach Space Theory Mathematical Analysis and Transform Methods

Identifiers

DOI: 10.1155/2012/649848

Citations and references

Cited by 4 15 references

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