0000000000462478

AUTHOR

Juho Nuutinen

showing 3 related works from this author

The Besov capacity in metric spaces

2016

We study a capacity theory based on a definition of Haj{\l} asz-Besov functions. We prove several properties of this capacity in the general setting of a metric space equipped with a doubling measure. The main results of the paper are lower bound and upper bound estimates for the capacity in terms of a modified Netrusov-Hausdorff content. Important tools are $\gamma$-medians, for which we also prove a new version of a Poincar\'e type inequality.

Discrete mathematicsGeneral Mathematics010102 general mathematicsType inequalitykapasiteetti01 natural sciencesMeasure (mathematics)Upper and lower boundsmetriset avaruudetFunctional Analysis (math.FA)Theory basedMathematics - Functional Analysis010101 applied mathematicsMetric spaceBesov spacesContent (measure theory)FOS: Mathematics0101 mathematicsMathematics
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On the continuity of discrete maximal operators in Sobolev spaces

2014

We investigate the continuity of discrete maximal operators in Sobolev space W 1;p (R n ). A counterexample is given as well as it is shown that the continuity follows under certain sucient assumptions. Especially, our research verifies that for the continuity in Sobolev spaces the role of the partition of the unity used in the construction of the maximal operator is very delicate.

Discrete mathematicsSobolev spaceGeneral Mathematicsta111Maximal operatorPartition (number theory)Modulus of continuityCounterexampleSobolev inequalitySobolev spaces for planar domainsMathematicsAnnales Academiae Scientiarum Fennicae Mathematica
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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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