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Volume 29, Issue 1
Some Estimates for Commutators of Fractional Integrals Associated to Operators with Gaussian Kernel Bounds on Weighted Morrey Spaces

H. Wang

Anal. Theory Appl., 29 (2013), pp. 72-85.

Published online: 2013-03

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  • Abstract

Let $L$ be the infinitesimal generator of an analytic semigroup on $L^2(\mathbf R^n)$ with Gaussian kernel bound, and let $L^{-\alpha/2}$ be the fractional integrals of $L$ for $0 < \alpha < n$. In this paper, we will obtain some boundedness properties of commutators $\big[b,L^{-\alpha/2}\big]$ on weighted Morrey spaces $L^{p,\kappa}(w)$ when the symbol $b$ belongs to $BMO(\mathbf R^n)$ or the homogeneous Lipschitz space.

  • AMS Subject Headings

42B20, 42B35

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COPYRIGHT: © Global Science Press

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@Article{ATA-29-72, author = {}, title = {Some Estimates for Commutators of Fractional Integrals Associated to Operators with Gaussian Kernel Bounds on Weighted Morrey Spaces}, journal = {Analysis in Theory and Applications}, year = {2013}, volume = {29}, number = {1}, pages = {72--85}, abstract = {

Let $L$ be the infinitesimal generator of an analytic semigroup on $L^2(\mathbf R^n)$ with Gaussian kernel bound, and let $L^{-\alpha/2}$ be the fractional integrals of $L$ for $0 < \alpha < n$. In this paper, we will obtain some boundedness properties of commutators $\big[b,L^{-\alpha/2}\big]$ on weighted Morrey spaces $L^{p,\kappa}(w)$ when the symbol $b$ belongs to $BMO(\mathbf R^n)$ or the homogeneous Lipschitz space.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2013.v29.n1.8}, url = {http://global-sci.org/intro/article_detail/ata/4516.html} }
TY - JOUR T1 - Some Estimates for Commutators of Fractional Integrals Associated to Operators with Gaussian Kernel Bounds on Weighted Morrey Spaces JO - Analysis in Theory and Applications VL - 1 SP - 72 EP - 85 PY - 2013 DA - 2013/03 SN - 29 DO - http://doi.org/10.4208/ata.2013.v29.n1.8 UR - https://global-sci.org/intro/article_detail/ata/4516.html KW - Gaussian upper bound, fractional integral, weighted Morrey space, commutator. AB -

Let $L$ be the infinitesimal generator of an analytic semigroup on $L^2(\mathbf R^n)$ with Gaussian kernel bound, and let $L^{-\alpha/2}$ be the fractional integrals of $L$ for $0 < \alpha < n$. In this paper, we will obtain some boundedness properties of commutators $\big[b,L^{-\alpha/2}\big]$ on weighted Morrey spaces $L^{p,\kappa}(w)$ when the symbol $b$ belongs to $BMO(\mathbf R^n)$ or the homogeneous Lipschitz space.

H. Wang. (1970). Some Estimates for Commutators of Fractional Integrals Associated to Operators with Gaussian Kernel Bounds on Weighted Morrey Spaces. Analysis in Theory and Applications. 29 (1). 72-85. doi:10.4208/ata.2013.v29.n1.8
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