Search results for "trace space"

showing 2 items of 2 documents

Dyadic Norm Besov-Type Spaces as Trace Spaces on Regular Trees

2019

In this paper, we study function spaces defined via dyadic energies on the boundaries of regular trees. We show that correct choices of dyadic energies result in Besov-type spaces that are trace spaces of (weighted) first order Sobolev spaces.

Pure mathematicsFunction spacetrace spaceMathematics::Analysis of PDEsMathematics::Classical Analysis and ODEs01 natural sciencesPotential theoryfunktioteoriaregular treeFOS: Mathematicsdyadic norm0101 mathematicsMathematics46E35 30L05Mathematics::Functional Analysis010102 general mathematicsFirst orderFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsSobolev spaceNorm (mathematics)Besov-type spacepotentiaaliteoriafunktionaalianalyysiAnalysisPotential Analysis
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Local maximal operators on fractional Sobolev spaces

2016

In this note we establish the boundedness properties of local maximal operators MG on the fractional Sobolev spaces Ws;p(G) whenever G is an open set in Rn, 0 < s < 1 and 1 < p < 1. As an application, we characterize the fractional (s;p)-Hardy inequality on a bounded open set by a Maz'ya-type testing condition localized to Whitney cubes. pq(G) whenever G is an open set in R n , 0 < s < 1 and 1 < p;q <1. Our main focus lies in the mapping properties of MG on a fractional Sobolev space W s;p (G) with 0 < s < 1 and 1 < p < 1, see Section 2 for the denition or (3) for a survey of this space. The intrinsically dened function space W s;p (G) on a given domain G coincides with the trace space F s …

Trace spaceFunction spaceGeneral MathematicsOpen setSpace (mathematics)01 natural sciencesDomain (mathematical analysis)CombinatoricsHardy inequality0103 physical sciencesClassical Analysis and ODEs (math.CA)FOS: Mathematics46E350101 mathematicsfractional Sobolev spaceMathematicsMathematics::Functional Analysista111010102 general mathematicsMathematical analysis42B25 46E35 47H99Functional Analysis (math.FA)Mathematics - Functional AnalysisSobolev spaceSection (category theory)Mathematics - Classical Analysis and ODEsBounded function47H99010307 mathematical physics42B25local maximal operator
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