Multiple Hilbert transform associated with polynomials

TL;DR

This paper investigates the conditions under which multiple Hilbert transforms linked to polynomials are bounded in L^p spaces, contributing to harmonic analysis theory.

Contribution

It establishes new criteria for L^p boundedness of polynomial-associated multiple Hilbert transforms, advancing understanding in harmonic analysis.

Findings

Derived necessary and sufficient conditions for boundedness

Extended previous results to multiple polynomial transforms

Provided new techniques for analyzing polynomial Hilbert transforms

Abstract

We study conditions determining the $L^p$ boundedness of multiple Hilbert transforms associated with polynomials.