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 Lp-improving estimates for associated multilinear generalized Radon transforms. Some of our results are new even in the convolution case.

Keywords
generalized Radon transform, affine arclength
Mathematical Subject Classification 2010
Primary: 42B99
Milestones
Received: 27 November 2013
Accepted: 9 June 2014
Published: 27 September 2014
Authors
Betsy Stovall
Department of Mathematics
University of Wisconsin
480 Lincoln Dr.
Madison, WI 53706-1325
United States