Notes on pseudodifferential operators commutators and Lipschitz functions

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 Lp(Rn){L}^{p}\left({{\bf{R}}}^{n}) into the homogeneous Triebel-Lizorkin space F˙pγ,∞(Rn){\dot{F}}_{p}^{\gamma ,\infty }\left({{\bf{R}}}^{n}) and from Lp(Rn){L}^{p}\left({{\bf{R}}}^{n}) into Lq(Rn){L}^{q}\left({{\bf{R}}}^{n}).

Keywords

• pseudodifferential operators
• commutators
• lipschitz functions
• homogeneous triebel-lizorkin space f˙pγ,∞ (rn)
• 47g30
• 42b35
• 42b25