Sharp weighted norm inequalities for singular integrals with non–smooth kernels

Abstract

In this paper, we prove the sharp weighted bound for certain singular integrals which have non-smooth kernels and do not belong to the class of standard Calderon–Zygmund operators. Our assumptions are weaker than those known in literature, since in particular we do not assume the Cotlar type inequality condition. Applications include sharp weighted estimates for the Riesz transforms associated to the Dirichlet Laplacians on open connected domains, the Riesz transforms associated to the Schrodinger operators with real potentials on the Euclidean spaces, the Riesz transforms associated to the degenerate Schrodinger operators and the Riesz transforms associated to the Schrodinger operators with inverse square potentials.