Endpoint Estimates for Commutators of Fractional Integrals Associated to Operators with Heat Kernel Bounds
Year: 2017
Author: Xianjun Liu, Wenming Li, Xuefang Yan
Communications in Mathematical Research , Vol. 33 (2017), Iss. 1 : pp. 73–84
Abstract
Let $L$ be the infinitesimal generator of an analytic semigroup on $L^2({\bf R}^n)$ with pointwise upper bounds on heat kernel, and denote by $L^{-\alpha/2}$ the fractional integrals of L. For a BMO function $b(x)$, we show a weak type $L{\rm log}L$ estimate of the commutators $[b,\ L^{-\alpha/2}](f)(x)=b(x)L^{-\alpha/2}(f)(x)-L^{-\alpha/2}(bf)(x)$. We give applications to large classes of differential operators such as the Schrödinger operators and second-order elliptic operators of divergence form.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2017.01.08
Communications in Mathematical Research , Vol. 33 (2017), Iss. 1 : pp. 73–84
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: fractional integral commutator $L{\rm log}L$ estimate semigroup sharp maximal function