A new characterization of the Riesz potential spaces with the aid of a composite wavelet transform

Sezer S., Aliev I. A.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.372, no.2, pp.549-558, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 372 Issue: 2
  • Publication Date: 2010
  • Doi Number: 10.1016/j.jmaa.2010.07.009
  • Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.549-558
  • Keywords: Fractional integrals, Riesz potentials, Wavelet transform, Semigroup, Riesz potential spaces, Inversion formulas, PARABOLIC POTENTIALS, INVERSION, INTEGRALS
  • Akdeniz University Affiliated: Yes

Abstract

We introduce a composite wavelet-like transform generated by the so-called beta-semigroup and a wavelet measure. This wavelet-like transform enables one to obtain a new explicit inversion formula for the Riesz potentials and a new characterization of the Riesz potential spaces. The usage of the concept "beta-semigroup", which is a natural generalization of the well-known Gauss-Weierstrass and Poisson semigroups, enables one to minimize the number of conditions on wavelet measure, no matter how big the order of Riesz's potentials is. 

We introduce a composite wavelet-like transform generated by the so-called beta-semigroup and a wavelet measure. This wavelet-like transform enables one to obtain a new explicit inversion formula for the Riesz potentials and a new characterization of the Riesz potential spaces. The usage of the concept "beta-semigroup", which is a natural generalization of the well-known Gauss-Weierstrass and Poisson semigroups, enables one to minimize the number of conditions on wavelet measure, no matter how big the order of Riesz's potentials is. (C) 2010 Elsevier Inc. All rights reserved.