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

Abstract

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 $L^p(\RN)$ as $p$ becomes large, and the growth of the $A_p$ constant on estimates of the area integrals on the weighted $L^p$ spaces.

30 pages

References in corpus (2)

• Gaussian heat kernel upper bounds via Phragmén-Lindelöf theorem
• Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part I: General operator theory and weights

Cited by in corpus (1)

• End-point estimates for singular integrals with non-smooth kernels on product spaces