The boundedness of variation associated with the commutators of approximate identities

Abstract

Abstract In this paper, we establish L p $L^{p}$ -boundedness and endpoint estimates for variation associated with the commutators of approximate identities, which are new for variation operators. As corollaries, we obtain the corresponding boundedness results for variation associated with the commutators of heat semigroups and Poisson semigroups.

Keywords

• Variation
• Boundedness
• Commutators