## Abstract and Applied Analysis

### Commutator Theorems for Fractional Integral Operators on Weighted Morrey Spaces

#### Abstract

Let $L$ be the infinitesimal generator of an analytic semigroup on ${L}^{\mathrm{2}}({\mathbb{R}}^{n})$ with Gaussian kernel bounds, and let ${L}^{-\alpha /\mathrm{2}}$ be the fractional integrals of $L$ for $\mathrm{0}<\alpha . For any locally integrable function $b$, the commutators associated with ${L}^{-\alpha /\mathrm{2}}$ are defined by $[b,{L}^{-\alpha /\mathrm{2}}](f)(x)=b(x){L}^{-\alpha /\mathrm{2}}(f)(x)-{L}^{-\alpha /\mathrm{2}}(bf)(x)$. When $b\in \text{B}\text{M}\text{O}(\omega )$ (weighted $\text{B}\text{M}\text{O}$ space) or $b\in \text{B}\text{M}\text{O}$, the authors obtain the necessary and sufficient conditions for the boundedness of $[b,{L}^{-\alpha /\mathrm{2}}]$ 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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