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## Universal <i>L<sup>p</sup></i> improving for averages along polynomial curves in low dimensions

### Abstract

We prove sharp <i>L<sup>p</sup></i> → <i>L<sup>q</sup></i> estimates for averaging operators along general polynomial curves in two and three dimensions. These operators are translation-invariant, given by convolution with the so-called affine arclength measure of the curve and we obtain universal bounds over the class of curves given by polynomials\ud of bounded degree. Our method relies on a geometric inequality for general vector polynomials together with a combinatorial argument due to M. Christ. Almost sharp Lorentz space estimates are obtained as well

Topics: QA
Publisher: Elsevier
Year: 2009
OAI identifier: oai:eprints.gla.ac.uk:24856
Provided by: Enlighten

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