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

Spyridon Dendrinos, Norberto Laghi, James Wright

Research output: Contribution to journalArticlepeer-review

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. (C) 2009 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)1355-1378
Number of pages24
JournalJournal of functional analysis
Volume257
Issue number5
DOIs
Publication statusPublished - 1 Sep 2009

Keywords

  • Averaging operators
  • Polynomial curves
  • Universal bounds
  • FOURIER RESTRICTION-THEOREMS
  • AFFINE ARCLENGTH MEASURES
  • DEGENERATE CURVES
  • CONVOLUTION-OPERATORS
  • OSCILLATORY INTEGRALS
  • R-3
  • SURFACES
  • PLANE
  • TRANSFORMS
  • REVOLUTION

Cite this