The $L^p$-to-$L^q$ Compactness of Commutators with $p>q$

Tuomas Hytönen, Kangwei Li, Jin Tao +1

Let $1<q<p<\infty$, $\frac{1}{r}:=\frac{1}{q}-\frac{1}{p}$, and $T$ be a non-degenerate Calderón--Zygmund operator. We show that the commutator $[b,T]$ is compact from $L^p({\mathbb{R}}^n)$ to…