Weighted Lp estimates for the area integral associated with self-adjoint operators on homogeneous space

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 L-p (X) as p becomes large. (C) 2012 Elsevier Inc. All rights reserved.