MAXIMAL POTENTIALS, MAXIMAL SINGULAR INTEGRALS, AND THE SPHERICAL MAXIMAL FUNCTION

摘要

We introduce a notion of maximal potentials and we prove that they form bounded operators from L~p to the homogeneous Sobolev space W~(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.