Title: Domination of multilinear singular integrals by positive sparse forms
Abstract:
A recent remarkable discovery in singular integral theory is a pointwise domination by sparse operators of linear and multilinear Calder\'on-Zygmund operators obtained by Lacey, Lerner, Lerner-Nazarov. Such domination carries a significant amount of information on the operators and often yields directly sharp weighted norm inequalities. In this talk, I would like to discuss a new result, jointly with A. Culiuc and F. Di Plinio, where we formulate a similar principle for a class of multilinear multiplier operators studied by Muscalu-Tao-Thiele including the bilinear Hilbert transform, and obtain a family of multilinear weighted bounds for this class of operators, which seems to be the first of its kind. The proof relies heavily on some new embedding theorems in the framework of the outer Lp theory developed by Do-Thiele.