Quantitative weighted estimates for singular integrals and commutators
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In this dissertation several quantitative weighted estimates for singular integral op- erators, commutators and some vector valued extensions are obtained. In particular strong and weak type $(p, p)$ estimates, Coifman-Fe erman estimates, Fe erman-Stein estimates, Bloom type estimates and endpoint estimates are provided. Most of the proofs of those results rely upon suitable sparse domination results that are provided as well in this dissertation. Also, as an application of the sparse estimates, local ex- ponential decay estimates are revisited, providing new proofs and results for vector valued extensions.