On commutators of fractional integrals
On commutators of fractional integrals
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 $0<\alpha < n$. For a BMO function $b(x)$ on ${\mathbb R}^n$, we show boundedness of the commutators $[b, L^{-\alpha /2}](f)(x)= b(x)L^{-\alpha /2}(f)(x)-L^{-\alpha …