Uniform Lp-improving for weighted averages on curves

Stovall, Betsy

doi:10.2140/apde.2014.7.1109

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

Betsy Stovall

Vol. 7 (2014), No. 5, 1109–1136

DOI: 10.2140/apde.2014.7.1109

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.

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

Vol. 7, No. 5, 2014