Work

Domination of multilinear singular integrals by positive sparse forms

Year: 2018

Type: article

Abstract: We establish a uniform domination of the family of trilinear multiplier forms with singularity over a one-dimensional subspace by positive sparse forms involving L p -averages. This class includes the adjoint forms to the bilinear Hilbert transforms. Our result strengthens the L p -boundedness proved by Muscalu, Tao and Thiele, and entails as a corollary a novel rich multilinear weighted theory. A particular case of this theory is the L q ( v 1 ) × L q ( v 2 ) -boundedness of the bilinear Hilbert transform when the weight v j belong to the class A q + 1 2 ∩ R H 2 . Our proof relies on a stopping time construction based on newly developed localized outer- L p embedding theorems for the wave packet transform. In the Appendix, we show how our domination principle can be applied to recover the vector-valued bounds for the bilinear Hilbert transforms recently proved by Benea and Muscalu.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.12139

Authors: Amalia Culiuc, Francesco Di Plinio, Yumeng Ou

Institutions: Georgia Institute of Technology, University of Virginia, Massachusetts Institute of Technology

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Endpoint Behavior of Modulation Invariant Singular Integrals, Endpoint Behavior of Modulation Invariant Singular Integrals