The convergence rate of truncated hypersingular integrals generated by the modified Poisson semigroup
JOURNAL OF INEQUALITIES AND APPLICATIONS, vol.2020, no.1, 2020 (SCI-Expanded, Scopus)
- 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
- Open Archive Collection: AVESIS Open Access Collection
- 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.