Search results for "Dyadic cubes"

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Existence of doubling measures via generalised nested cubes

2012

Working on doubling metric spaces, we construct generalised dyadic cubes adapting ultrametric structure. If the space is complete, then the existence of such cubes and the mass distribution principle lead into a simple proof for the existence of doubling measures. As an application, we show that for each $\epsilon>0$ there is a doubling measure having full measure on a set of packing dimension at most $\epsilon$.

Applied MathematicsGeneral MathematicsDyadic cubesStructure (category theory)Space (mathematics)Measure (mathematics)CombinatoricsMetric spacePacking dimension28C15 (Primary) 54E50 (Secondary)Mathematics - Classical Analysis and ODEsSimple (abstract algebra)Classical Analysis and ODEs (math.CA)FOS: MathematicsUltrametric spaceMathematicsProceedings of the American Mathematical Society
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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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