Multilinear singular integral forms of Christ-Journ\'e type

TL;DR

This paper establishes polynomial growth estimates for Christ-Journé multilinear singular integral forms across multiple Lebesgue spaces, extending the understanding of their boundedness properties.

Contribution

It provides new polynomial growth bounds for multilinear singular integrals of Christ-Journé type, generalizing previous results to broader settings.

Findings

Proved polynomial growth estimates for Christ-Journé multilinear forms

Extended boundedness results to more general multilinear singular integrals

Enhanced understanding of the behavior of multilinear singular integrals in Lebesgue spaces

Abstract

We prove $L^{p_1}(\mathbb R^d)\times \dots \times L^{p_{n+2}}(\mathbb R^{d})$ polynomial growth estimates for the Christ-Journ\'e multilinear singular integral forms and suitable generalizations.