Sharp weighted norm inequalities for singular integrals with non–smooth kernels
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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 Calderón–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 Schrödinger operators with real potentials on the Euclidean spaces, the Riesz transforms associated to the degenerate Schrödinger operators and the Riesz transforms associated to the Schrödinger operators with inverse square potentials.
KeywordsHeat kernels Singular operators Weighted estimates
Mathematics Subject Classification58J35 42B20
Xuan Thinh Duong was supported by Australian Research Council through the ARC grant DP160100153.