2020 Two-Weight, Weak-Type Norm Inequalities for Fractional Integral Operators and Commutators on Weighted Morrey and Amalgam Spaces
Hua Wang
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Abstr. Appl. Anal. 2020: 1-23 (2020). DOI: 10.1155/2020/3235942

Abstract

Let 0<γ<n and Iγ be the fractional integral operator of order γ,Iγf(x)=n|xy|γnf(y)dy and let [b,Iγ] be the linear commutator generated by a symbol function b and Iγ,[b,Iγ]f(x)=b(x)·Iγf(x)Iγ(bf)(x). This paper is concerned with two-weight, weak-type norm estimates for such operators on the weighted Morrey and amalgam spaces. Based on weak-type norm inequalities on weighted Lebesgue spaces and certain Ap-type conditions on pairs of weights, we can establish the weak-type norm inequalities for fractional integral operator Iγ as well as the corresponding commutator in the framework of weighted Morrey and amalgam spaces. Furthermore, some estimates for the extreme case are also obtained on these weighted spaces.

Acknowledgments

This work was done while the author was visiting Memorial University of Newfoundland in Canada. The author wishes to thank Prof. Jie Xiao for the invitation and the warm hospitality during his visit.

Citation

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Hua Wang. "Two-Weight, Weak-Type Norm Inequalities for Fractional Integral Operators and Commutators on Weighted Morrey and Amalgam Spaces." Abstr. Appl. Anal. 2020 1 - 23, 2020. https://doi.org/10.1155/2020/3235942

Information

Received: 23 June 2019; Accepted: 17 December 2019; Published: 2020
First available in Project Euclid: 28 July 2020

Digital Object Identifier: 10.1155/2020/3235942

Rights: Copyright © 2020 Hindawi

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