The convergence rate of truncated hypersingular integrals generated by the modified Poisson semigroup


Creative Commons License

ERYİĞİT M., Evcan S., ÇOBANOĞLU S.

JOURNAL OF INEQUALITIES AND APPLICATIONS, vol.2020, no.1, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2020 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.1186/s13660-020-02468-9
  • Journal Name: JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Truncated hypersingular integrals, Flett potentials, Poisson semigroup, Rate of convergence, BESSEL POTENTIALS, INVERSION, SPACES, AID, RIESZ
  • Akdeniz University Affiliated: Yes

Abstract

Hypersingular integrals have appeared as effective tools for inversion of multidimensional potential-type operators such as Riesz, Bessel, Flett, parabolic potentials, etc. They represent (at least formally) fractional powers of suitable differential operators. In this paper the family of the so-called "truncated hypersingular integral operators" D(epsilon)(alpha)f is introduced, that is generated by the modified Poisson semigroup and associated with the Flett potentials F-alpha phi = (E + root-Delta)(-alpha)phi (0 < alpha < infinity, phi is an element of L-p(R-n)). Then the relationship between the order of "L-p-smoothness" of a function f and the "rate of L-p-convergence" of the families D(epsilon)(alpha)F(alpha)f to the function f as epsilon -> 0(+) is also obtained.