6533b833fe1ef96bd129b58c
RESEARCH PRODUCT
Maximal potentials, maximal singular integrals, and the spherical maximal function
Piotr HajłaszZhuomin LiuZhuomin Liusubject
Sobolev spaceMathematics::Functional AnalysisHomogeneousApplied MathematicsGeneral MathematicsBounded functionMathematical analysisMathematics::Analysis of PDEsMaximal operatorMaximal functionSingular integralMathematicsSobolev inequalitydescription
We introduce a notion of maximal potentials and we prove that they form bounded operators from L to the homogeneous Sobolev space Ẇ 1,p for all n/(n − 1) < p < n. We apply this result to the problem of boundedness of the spherical maximal operator in Sobolev spaces.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-07-31 | Proceedings of the American Mathematical Society |