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2012 Necessary and Sufficient Conditions for Boundedness of Commutators of the General Fractional Integral Operators on Weighted Morrey Spaces
Zengyan Si, Fayou Zhao
Abstr. Appl. Anal. 2012: 1-14 (2012). DOI: 10.1155/2012/929381

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.

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Zengyan Si. Fayou Zhao. "Necessary and Sufficient Conditions for Boundedness of Commutators of the General Fractional Integral Operators on Weighted Morrey Spaces." Abstr. Appl. Anal. 2012 1 - 14, 2012. https://doi.org/10.1155/2012/929381

Information

Published: 2012
First available in Project Euclid: 14 December 2012

zbMATH: 1256.42024
MathSciNet: MR2965481
Digital Object Identifier: 10.1155/2012/929381

Rights: Copyright © 2012 Hindawi

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