Necessary and Sufficient Conditions for Boundedness of Commutators of the General Fractional Integral Operators on Weighted Morrey Spaces

Abstract and Applied Analysis. 2012;2012 DOI 10.1155/2012/929381

 

Journal Homepage

Journal Title: Abstract and Applied Analysis

ISSN: 1085-3375 (Print); 1687-0409 (Online)

Publisher: Hindawi Publishing Corporation

LCC Subject Category: Science: Mathematics

Country of publisher: Egypt

Language of fulltext: English

Full-text formats available: PDF, HTML, ePUB, XML

 

AUTHORS

Zengyan Si (School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China)
Fayou Zhao (Department of Mathematics, Shanghai University, Shanghai 200444, China)

EDITORIAL INFORMATION

Blind peer review

Editorial Board

Instructions for authors

Time From Submission to Publication: 27 weeks

 

Abstract | Full Text

We prove that b is in Lipβ(ω) if and only if the commutator [b,L-α/2] of the multiplication operator by b and the general fractional integral operator L-α/2 is bounded from the weighted Morrey space Lp,k(ω) to Lq,kq/p(ω1-(1-α/n)q,ω), where 0<β<1, 0<α+β<n,1<p<n/(α+β), 1/q=1/p-(α+β)/n, 0≤k<p/q, ωq/p∈A1, and rω>(1-k)/(p/(q-k)), and here rω denotes the critical index of ω for the reverse Hölder condition.