Weighted L p estimates for the area integral associated to self-adjoint operators

This article is concerned with some weighted norm inequalities for the so-called horizontal (i.e., involving time derivatives) area integrals associated to a non-negative self-adjoint operator satisfying a pointwise Gaussian estimate for its heat kernel, as well as the corresponding vertical (i.e., involving space derivatives) area integrals associated to a non-negative self-adjoint operator satisfying in addition a pointwise upper bounds for the gradient of the heat kernel. As applications, we obtain sharp estimates for the operator norm of the area integrals on ${L^p(\mathbb{R}^N)}$ as p becomes large, and the growth of the A _p constant on estimates of the area integrals on the weighted L ^p spaces.