Weighted [formula omitted] estimates for the area integral associated with self-adjoint operators on homogeneous space

Abstract

Let X be a metric space with doubling measure, and L be a non-negative self-adjoint operator such that the corresponding heat kernels satisfy Gaussian bounds. This article is concerned with some weighted norm inequalities for area integrals associated with L. As an application, we obtain sharp estimates for the operator norm of the area integrals on Lp(X) as p becomes large.