Generalized Riesz Potential Spaces and their Characterization via Wavelet-Type Transform

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ALİYEV İ., Saglik E.

FILOMAT, vol.30, no.10, pp.2809-2823, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 10
  • Publication Date: 2016
  • Doi Number: 10.2298/fil1610809a
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2809-2823
  • Keywords: Wavelet-type transform, generalized Riesz potentials, Riesz potential spaces, semigroup, generalized translation operator
  • Akdeniz University Affiliated: Yes

Abstract

We introduce a wavelet-type transform generated by the so-called beta-semigroup, which is a natural generalization of the Gauss-Weierstrass and Poisson semigroups associated to the Laplace-Bessel convolution. By making use of this wavelet-type transform we obtain new explicit inversion formulas for the generalized Riesz potentials and a new characterization of the generalized Riesz potential spaces. We show that the usage of the concept beta-semigroup gives rise to minimize the number of conditions on wavelet measure, no matter how big the order of the generalized Riesz potentials is.