Search results for "fractional maximal function"

showing 2 items of 2 documents

Smoothing properties of the discrete fractional maximal operator on Besov and Triebel-Lizorkin spaces

2013

Motivated by the results of Korry, and Kinnunen and Saksman, we study the behaviour of the discrete fractional maximal operator on fractional Hajlasz spaces, Hajlasz-Besov, and Hajlasz-Triebel-Lizorkin spaces on metric measure spaces. We show that the discrete fractional maximal operator maps these spaces to the spaces of the same type with higher smoothness. Our results extend and unify aforementioned results. We present our results in a general setting, but they are new already in the Euclidean case.

Pure mathematicsGeneral MathematicsMetric measure spaceSpace (mathematics)Triebel–Lizorkin spaceMeasure (mathematics)Triebel-Lizorkin spaceFOS: Mathematics46E35Birnbaum–Orlicz spaceLp spaceBesov spacefractional Sobolev spaceMathematicsMathematics::Functional Analysista111Mathematical analysisFractional Sobolev spaceFunctional Analysis (math.FA)Fractional calculusMathematics - Functional Analysismetric measure space42B25 46E35fractional maximal functionBesov spaceInterpolation spaceFractional maximal function42B25
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Fractional Maximal Functions in Metric Measure Spaces

2013

Abstract We study the mapping properties of fractional maximal operators in Sobolev and Campanato spaces in metric measure spaces. We show that, under certain restrictions on the underlying metric measure space, fractional maximal operators improve the Sobolev regularity of functions and map functions in Campanato spaces to Hölder continuous functions. We also give an example of a space where fractional maximal function of a Lipschitz function fails to be continuous.

fractional sobolev spacePure mathematicsQA299.6-433Applied MathematicsMathematics::Classical Analysis and ODEsMathematics::Analysis of PDEsSpace (mathematics)Lipschitz continuityMeasure (mathematics)Functional Analysis (math.FA)Sobolev spaceMathematics - Functional Analysiscampanato space42B25 46E35metric measure spaceMetric (mathematics)FOS: Mathematicsfractional maximal function46e35Maximal functionGeometry and Topology42b25AnalysisMathematicsAnalysis and Geometry in Metric Spaces
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