6533b854fe1ef96bd12af66c
RESEARCH PRODUCT
Fractional Maximal Functions in Metric Measure Spaces
Heli TuominenToni HeikkinenJuho NuutinenJuha Lehrbäcksubject
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 Topology42b25AnalysisMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-01-30 | Analysis and Geometry in Metric Spaces |