Universal L^p improving for averages along polynomial curves in low dimensions

Dendrinos, S., Laghi, N. and Wright, J. (2009) Universal L^p improving for averages along polynomial curves in low dimensions. Journal of Functional Analysis, 257(5), pp. 1355-1378. (doi: 10.1016/j.jfa.2009.05.011)

Abstract

We prove sharp L^p → L^q 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 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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Dendrinos, Dr Spyridon
• Authors: Dendrinos, S., Laghi, N., and Wright, J.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Research Group: Analysis
• Journal Name: Journal of Functional Analysis
• Journal Abbr.: J. Funct. Anal.
• Publisher: Elsevier
• ISSN: 0022-1236
• ISSN (Online): 1096-0783
• Published Online: 09 June 2009
• Copyright Holders: Copyright © 2009 Elsevier
• First Published: First published in Journal of Functional Analysis 257(5):1355-1378
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher.