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

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.

arXiv commentThis is a preprint version of a published article. The final version is in Anal. PDE 7 (2014), no. 5, 1109-1136