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 - <p style="text-align: justify;">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 $0 &lt; \alpha &lt; n$. 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.</p>