Estimates for multilinear commutators of generalized fractional integral operators on weighted Morrey spaces

Abstract

Let $L$ be the infinitesimal generator of an analytic semigroup on $L^2({\mathbb{R}}^n)$ with Gaussian kernel bounds, and let $L^{-\alpha /2}$ be the fractional integrals of $L$ for $0<\alpha <n$. Assume that $\vec{b}=(b_1,b_2,\cdots ,b_m)$ is a finite family of locally integrable functions, then the multilinear commutators generated by $\vec{b}$ and $L^{-\alpha /2}$ is defined by \begin{equation*} L_{\vec{b}}^{-α/2}f=[b_m,\cdots,[b_2,[b_1,L^{-α/2}]],\cdots,]f \end{equation*} when $b_j\in BMO(w)$, $j=1,2,\cdots ,m$, the authors obtain the boundedness of $L_{\vec{b}}^{-\alpha /2}$ on weighted Morrey spaces.

16 pages. arXiv admin note: text overlap with arXiv:1203.4407 by other authors

References in corpus (4)

• Intrinsic square functions on the weighted Morrey spaces
• Some estimates for commutators of fractional integral operators on weighted Morrey spaces
• Necessary and sufficient conditions for boundedness of commutators of the general fractional integral operators on weighted Morrey spaces
• Commutator Theorems for Fractional Integral Operators on Weighted Morrey Spaces