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Local maximal operators on fractional Sobolev spaces
Antti V. VähäkangasHannes Luirosubject
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 operatordescription
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 pp(G) if and only if G is regular, i.e.,jB(x;r)\Gj' r n
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-07-01 |