Yumeng Ou

Domination of multilinear singular integrals by positive sparse forms

We establish a uniform domination of the family of trilinear multiplier forms with singularity over a one-dimensional subspace by positive sparse forms involving

A T(b) theorem on product spaces

L^p

UPPER BOUND FOR MULTI-PARAMETER ITERATED COMMUTATORS

-averages. This class includes the adjoint forms to the bilinear Hilbert transforms. Our result strengthens the

Product BMO, Little BMO, and Riesz Commutators in the Bessel Setting

L^p

A modulation invariant Carleson embedding theorem outside local L 2

-boundedness proved in \cite{MTT} and entails as a corollary a rich multilinear weighted theory. In particular, we obtain

A sparse domination principle for rough singular integrals

L^{q_1}(v_1) \times L^{q_2}(v_2)

Higher order Journé commutators and characterizations of multi-parameter BMO

-boundedness of the bilinear Hilbert transform when the weights

Banach-valued multilinear singular integrals

v_j

Uniform sparse domination of singular integrals via dyadic shifts

belong to the class

Multi-parameter singular integral operators and representation theorem

A_{\frac{q+1}{2}}\cap RH_2