Abstract and Applied Analysis

Commutator Theorems for Fractional Integral Operators on Weighted Morrey Spaces

Zhiheng Wang and Zengyan Si

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Abstract

Let L be the infinitesimal generator of an analytic semigroup on L 2 ( R n ) with Gaussian kernel bounds, and let L - α / 2 be the fractional integrals of L for 0 < α < n . For any locally integrable function b , the commutators associated with L - α / 2 are defined by [ b , L - α / 2 ] ( f ) ( x ) = b ( x ) L - α / 2 ( f ) ( x ) - L - α / 2 ( b f ) ( x ) . When b B M O ( ω ) (weighted B M O space) or b B M O , the authors obtain the necessary and sufficient conditions for the boundedness of [ b , L - α / 2 ] on weighted Morrey spaces, respectively.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 413716, 8 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412277029

Digital Object Identifier
doi:10.1155/2014/413716

Mathematical Reviews number (MathSciNet)
MR3219370

Zentralblatt MATH identifier
07022347

Citation

Wang, Zhiheng; Si, Zengyan. Commutator Theorems for Fractional Integral Operators on Weighted Morrey Spaces. Abstr. Appl. Anal. 2014 (2014), Article ID 413716, 8 pages. doi:10.1155/2014/413716. https://projecteuclid.org/euclid.aaa/1412277029


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