Convolution estimates and model surfaces of low codimension

TL;DR

This paper presents measures on specific k-surfaces in R^d that nearly achieve optimal convolution estimates, advancing understanding of harmonic analysis on geometric structures.

Contribution

It provides new examples of measures on k-surfaces that satisfy nearly optimal convolution estimates, contributing to harmonic analysis and geometric measure theory.

Findings

Measures on k-surfaces with near-optimal convolution estimates

Examples that approach theoretical bounds in harmonic analysis

Insights into the structure of low codimension surfaces

Abstract

We give examples of measures on certain k-surfaces in R^d. These measures satisfy convolution estimates which are nearly optimal.