Abstract and Applied Analysis (Jan 2012)

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

  • Ravshan Ashurov,
  • Almaz Butaev,
  • Biswajeet Pradhan

DOI
https://doi.org/10.1155/2012/649848
Journal volume & issue
Vol. 2012

Abstract

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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 Lp 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.