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

Georgian Mathematical Journal, vol.27, no.4, pp.557-567, 2020 (Journal Indexed in SCI Expanded)

• Publication Type: Article / Article
• Volume: 27 Issue: 4
• Publication Date: 2020
• Doi Number: 10.1515/gmj-2018-0065
• Title of Journal : Georgian Mathematical Journal
• Page Numbers: pp.557-567
• Keywords: Hardy operator, Local Morrey-Lorentz space, Riesz potential

#### Abstract

© 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.In this paper, the necessary and sufficient conditions are found for the boundedness of the Riesz potential I α {I_{\alpha}} in the local Morrey-Lorentz spaces M p, q; λ loc Ã¢ÂÂ¢ (Ã¢âžÂ n) {M_{p,q;{\lambda}}{\mathrm{loc}}({\mathbb{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; λ loc Ã¢ÂÂ¢ (Ã¢âžÂ n) {M_{p,q;{\lambda}}{\mathrm{loc}}({\mathbb{R}{n}})}.