Dyadic-probabilistic methods in bilinear analysis

We demonstrate and develop dyadic–probabilistic methods in connection with non-homogeneous bilinear operators, namely singular integrals square functions. the full theory of using a modern point view. The main result is new global T b Tb theorem for Calderón–Zygmund operators this setting. Our tools include maximal truncations, adapted Cotlar type inequalities suppression big piece methods. While proving our results we also advance refine linear by improving techniques results. For example, simplify make more efficient some summing arguments appearing Baseline 1"> 1 encoding="application/x-tex">T1 proofs. As byproduct, can manage ease quite general modulus continuity kernel estimates. testing conditions are virtue method proof.