Sobolev and isoperimetric inequalities for Dirichlet forms on homogeneous spaces
The authors announce local embedding theorems of Sobolev, John-Nirenberg, and Campanato-Morrey type for Dirichlet forms on homogeneous spaces. The importance of these results is determined by their successful applications to selfadjoint subelliptic operators, to weighted uniformly elliptic operators, as well as to Dirichlet operators on certain self- similar fractals, like the ``Sierpinski gasket''.
scientific article; zbMATH DE number 817261