%0 Journal Article
%T Maximal potentials, maximal singular integrals, and the spherical maximal function
%A Piotr Hajlasz
%A Zhuomin Liu
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1306.6358v1