#### Vol. 7, No. 5, 2014

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

### Betsy Stovall

Vol. 7 (2014), No. 5, 1109–1136
##### 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.