Continuity for the one-dimensional centered Hardy-Littlewood maximal operator at the derivative level
Cristian González-Riquelme
Abstract
We prove the continuity of the map f↦(Mf)′ from W1,1(R) to L1(R), where M is the centered Hardy-Littlewood maximal operator. This solves a question posed by Carneiro, Madrid and Pierce.
Topics & Concepts
MathematicsOperator (biology)Derivative (finance)Hardy spaceMaximal operatorShift operatorPure mathematicsMathematical analysisCompact operatorBounded functionProgramming languageGeneFinancial economicsEconomicsComputer scienceTranscription factorBiochemistryExtension (predicate logic)ChemistryRepressorAdvanced Harmonic Analysis ResearchNonlinear Partial Differential EquationsHolomorphic and Operator Theory