Maximal potentials, maximal singular integrals, and the spherical maximal function

Abstract

We introduce a notion of maximal potentials and we prove that they form bounded operators from $L^p$ to the homogeneous Sobolev space ${\dot{W}}^{1,p}$ for all $n/(n-1)<p<n$. We apply this result to the problem of boundedness of the spherical maximal operator in Sobolev spaces.

Cited by in corpus (1)

• Sobolev spaces, Lebesgue points and maximal functions