Riesz potential in the local Morrey-Lorentz spaces and some applications

Guliyev V. S., Kucukaslan A., AYKOL KOCAKUŞAKLI C., ŞERBETÇİ A.

GEORGIAN MATHEMATICAL JOURNAL, vol.27, no.4, pp.557-567, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.1515/gmj-2018-0065
  • Journal Name: GEORGIAN MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.557-567
  • Keywords: Local Morrey-Lorentz space, Riesz potential, Hardy operator, SUFFICIENT CONDITIONS, INTEGRAL-OPERATORS, BOUNDEDNESS, HARDY
  • Ankara University Affiliated: Yes

Abstract

In this paper, the necessary and sufficient conditions are found for the boundedness of the Riesz potential I-alpha in the local Morrey- Lorentz spaces M-p,q(loc);lambda (R-n). This result is applied to the boundedness of particular operators such as the fractional maximal operator, fractional Marcinkiewicz operator and fractional powers of some analytic semigroups on the local Morrey-Lorentz spaces M-p,q(loc);lambda (R-n).