Regularity and continuity of commutators of the Hardy–Littlewood maximal function
Feng Liu, Qingying Xue, Pu Zhang
Abstract
Abstract Let M be the Hardy–Littlewood maximal function and let be its corresponding commutator. For and , we show that the commutator is bounded and continuous from Sobolev space to Sobolev space for when , from Triebel–Lizorkin space to if and from Besov space to if and .
Topics & Concepts
CommutatorMathematicsBounded mean oscillationSobolev spaceHardy spaceBounded functionSpace (punctuation)Pure mathematicsMathematical analysisMaximal functionFunction (biology)Besov spaceMeasurable functionInterpolation spaceFunctional analysisAlgebra over a fieldBiochemistryPhilosophyChemistryLie conformal algebraGeneBiologyEvolutionary biologyLinguisticsAdvanced Harmonic Analysis ResearchHolomorphic and Operator TheoryMathematical Analysis and Transform Methods