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, cilt.2020, sa.1, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2020 Sayı: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1186/s13660-020-02468-9
  • Dergi Adı: JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Derginin Tarandığı İndeksler: 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
  • Anahtar Kelimeler: Truncated hypersingular integrals, Flett potentials, Poisson semigroup, Rate of convergence, BESSEL POTENTIALS, INVERSION, SPACES, AID, RIESZ
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.