Translator Disclaimer
December 2021 Two-type estimates for the boundedness of generalized Riesz potential operator in the generalized weighted local Morrey spaces
Abdulhamit Kucukaslan
Adv. Studies: Euro-Tbilisi Math. J. 14(4): 111-134 (December 2021). DOI: 10.3251/asetmj/1932200817

Abstract

In this paper, we prove the Spanne-type boundedness of the generalized Riesz potential operator $I_{\rho}$ on the generalized weighted local Morrey spaces with $w^{q} \in A_{1+\frac{q}{p'}}$ for $1 \le p \le q \le \infty $ and including its the weak estimates with $w \in A_{1,q}$ for $1\le q\le\infty$. We also prove the Adams-type boundedness of the operator $I_{\rho}$ on the generalized weighted Morrey spaces with $ w \in A_{p,q}$ for $1\le p\le q \le \infty$ and also including its the weak estimates with $w \in A_{1,q}$ for $1\le q\le \infty$.

Funding Statement

The research of Abdulhamit Kucukaslan was supported by the grant of The Scientific and Technological Research Council of Turkey, Grant TUBITAK-1059B191600675.

Citation

Download Citation

Abdulhamit Kucukaslan. "Two-type estimates for the boundedness of generalized Riesz potential operator in the generalized weighted local Morrey spaces." Adv. Studies: Euro-Tbilisi Math. J. 14 (4) 111 - 134, December 2021. https://doi.org/10.3251/asetmj/1932200817

Information

Received: 23 August 2020; Accepted: 15 April 2021; Published: December 2021
First available in Project Euclid: 16 December 2021

Digital Object Identifier: 10.3251/asetmj/1932200817

Subjects:
Primary: 42B20
Secondary: 42B25 , 42B35

Keywords: generalized Riesz potential operator , generalized weighted local Morrey spaces , generalized weighted Morrey spaces , Muckenhoupt-Weeden classes

Rights: Copyright © 2021 Tbilisi Centre for Mathematical Sciences

JOURNAL ARTICLE
24 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.14 • No. 4 • December 2021
Back to Top