Uniform $L^p$-improving for weighted averages on curves

TL;DR

This paper introduces variable parameter affine arclength measures on curves and establishes near-optimal $L^p$-improving bounds for related multilinear Radon transforms, advancing understanding in harmonic analysis.

Contribution

It develops new variable parameter affine arclength measures and proves near-optimal $L^p$-improving estimates, including novel results even for convolution cases.

Findings

Established near-optimal $L^p$-improving estimates for multilinear Radon transforms.

Introduced variable parameter affine arclength measures on curves.

Extended results to convolution cases, providing new insights.

Abstract

We define variable parameter analogues of the affine arclength measure on curves and prove near-optimal $L^p$-improving estimates for associated multilinear generalized Radon transforms. Some of our results are new even in the convolution case.