Weighted Dirichlet-type inequalities for Steiner symmetrization

In this paper weighted Dirichlet-type inequalities for Steiner symmetrization are proved. Similar inequalities were known for the so-called starshaped rearrangements. Furthermore it is shown that the Steiner symmetrization is a mapping from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $W^{1,1} _+ ({\Bbb R}^n)$\end{document} into itself.