Grigori Karagulyan: On sparse domination of some operators in Harmonic Analysis

Abstract: We introduce a class of operators on abstract measurable spaces, which unifies variety of operators in Harmonic Analysis. We prove that such operators can be dominated by simple sparse operators. Those domination theorems imply some new estimations for Calderón-Zygmund operators, maximal functions, martingale transforms and Carleson operators.