Bellman function technique for multilinear estimates and an application to generalized paraproducts

Abstract

We prove L^p estimates for a class of two-dimensional multilinear forms that naturally generalize (dyadic variants of) both classical paraproducts and the twisted paraproduct introduced in [5] and studied in [1] and [6]. The method we use builds on the approach from [6] and we present it as a rather general technique for proving estimates on dyadic multilinear operators. In the particular application to "generalized paraproducts" this method is combined with combinatorics of integer partitions.

28 pages, 7 figures/diagrams/tables

Cited by in corpus (11)

• Norm-variation of ergodic averages with respect to two commuting transformations
• One modification of the martingale transform and its applications to paraproducts and stochastic integrals
• Quantitative norm convergence of double ergodic averages associated with two commuting group actions
• Singular Brascamp-Lieb inequalities with cubical structure
• Density theorems for anisotropic point configurations
• An $L^4$ estimate for a singular entangled quadrilinear form
• Cancellation for the multilinear Hilbert transform
• T(1) theorem for dyadic singular integral forms associated with hypergraphs
• Large dilates of hypercube graphs in the plane
• Coloring and density theorems for configurations of a given volume
• On a trilinear form related to the Carleson theorem