Search results for "Triebel-Lizorkin space"

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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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Traces of weighted function spaces: dyadic norms and Whitney extensions

2017

The trace spaces of Sobolev spaces and related fractional smoothness spaces have been an active area of research since the work of Nikolskii, Aronszajn, Slobodetskii, Babich and Gagliardo among others in the 1950's. In this paper we review the literature concerning such results for a variety of weighted smoothness spaces. For this purpose, we present a characterization of the trace spaces (of fractional order of smoothness), based on integral averages on dyadic cubes, which is well adapted to extending functions using the Whitney extension operator.

Pure mathematicsTrace (linear algebra)Function spaceGeneral MathematicsDyadic cubesTriebel-Lizorkin spacesweighted Sobolev spaces01 natural sciencesfunktioanalyysiOperator (computer programming)trace theoremsClassical Analysis and ODEs (math.CA)FOS: Mathematics46E350101 mathematicsfunktioavaruudetMathematicsSmoothness (probability theory)010102 general mathematicsExtension (predicate logic)010101 applied mathematicsSobolev spacesovellettu matematiikkaMathematics - Classical Analysis and ODEsBesov spacesVariety (universal algebra)
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