62 research outputs found
Matrix weights, degenerate Sobolev spaces, and mappings of finite distortion.
We study degenerate Sobolev spaces where the degeneracy is controlled by a matrix A_p weight. We prove that the classical Meyers-Serrin theorem, H = W, holds in this setting. As applications we prove partial regularity results for weak solutions of degenerate p-Laplacian equations, and in particular for mappings of finite distortion
The sharp weighted bound for multilinear maximal functions and Calder\'{o}n-Zygmund operators
We investigate the weighted bounds for multilinear maximal functions and
Calder\'on-Zygmund operators from to
, where with
and is a multiple weight. We
prove the sharp bound for the multilinear maximal function for all such
and prove the sharp bound for -linear Calder\'on-Zymund
operators when
- β¦