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


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Journal Title: Abstract and Applied Analysis

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

Publisher: Hindawi Limited

LCC Subject Category: Science: Mathematics

Country of publisher: United Kingdom

Language of fulltext: English

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


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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.