The solution of the Kato problem for degenerate elliptic operators with Gaussian bounds
Analysis of PDEs
2009-07-20 v1
Abstract
We prove the Kato conjecture for degenerate elliptic operators in R^n. More precisely, we consider the divergence form operator L_w = -1/w div (wA) grad, where w is a Muckenhoupt A_2 weight and A is a complex valued n x n matrix which is bounded and uniformly elliptic. We show that if the associated semigroup satisfies Gaussian upper bounds, then the Kato square root estimate holds.
Keywords
Cite
@article{arxiv.0907.2947,
title = {The solution of the Kato problem for degenerate elliptic operators with Gaussian bounds},
author = {D. Cruz-Uribe and C. Rios},
journal= {arXiv preprint arXiv:0907.2947},
year = {2009}
}