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

Let XX be a metric space with doubling measure, and LL 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 LL. As an application, we obtain sharp estimates for the operator norm of the area integrals on Lp(X)Lp(X) as pp becomes large.