Power-type cancellation for the simplex Hilbert transform

TL;DR

This paper establishes new L^p bounds for the truncated simplex Hilbert transform, showing that the bounds grow at a rate less than one power of the truncation range on a logarithmic scale.

Contribution

It provides the first power-type bounds for the truncated simplex Hilbert transform, advancing understanding of its behavior.

Findings

L^p bounds grow with a power less than one of the truncation range

Bounds are logarithmic in the truncation scale

Advances the theory of multilinear singular integrals

Abstract

We prove $\mathrm{L}^p$ bounds for the truncated simplex Hilbert transform which grow with a power less than one of the truncation range in the logarithmic scale.