Abstract and Applied Analysis

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

Zengyan Si and Fayou Zhao

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Abstract

We prove that b is in L i p β ( 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 L p , k ( ω ) to L q , k q / p ( ω 1 - ( 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 , ω q / p A 1, and r ω > (1 - k) / (p / ( q - k )) , and here r ω denotes the critical index of ω for the reverse Hölder condition.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 929381, 14 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1355495851

Digital Object Identifier
doi:10.1155/2012/929381

Mathematical Reviews number (MathSciNet)
MR2965481

Zentralblatt MATH identifier
1256.42024

Citation

Si, Zengyan; Zhao, Fayou. Necessary and Sufficient Conditions for Boundedness of Commutators of the General Fractional Integral Operators on Weighted Morrey Spaces. Abstr. Appl. Anal. 2012 (2012), Article ID 929381, 14 pages. doi:10.1155/2012/929381. https://projecteuclid.org/euclid.aaa/1355495851


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