Notes on pseudodifferential operators commutators and Lipschitz functions

Abstract

Abstract This article focuses on the boundedness of the commutators generated by pseudodifferential operators with Lipschitz functions and obtains a sufficient condition such that these operators are bounded from L p ( R n ) {L}^{p}\left({{\bf{R}}}^{n}) into the homogeneous Triebel-Lizorkin space F ˙ p γ , ∞ ( R n ) {\dot{F}}_{p}^{\gamma ,\infty }\left({{\bf{R}}}^{n}) and from L p ( R n ) {L}^{p}\left({{\bf{R}}}^{n}) into L q ( R n ) {L}^{q}\left({{\bf{R}}}^{n}) .