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

By S. Dendrinos, N. Laghi and J. Wright

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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Citations

  1. (2005). A non-linear generalisation of the LoomisWhitney inequality and applications, doi
  2. (1993). A remark on convolution with measures supported on curves, doi
  3. (2004). A uniform Fourier restriction theorem for ane surfaces in R3,
  4. (2007). An ane restriction estimate in R3,
  5. (1994). Convolution estimates for some degenerate curves, doi
  6. (1999). Convolution operators with the ane arclength measure on plane curves, doi
  7. (1999). Convolution with ane arclength measures in the plane,
  8. (2002). Convolution with measures on polynomial curves, doi
  9. (1998). Convolution, curvature and combinatorics: a case study,
  10. (1990). Degenerate curves and harmonic analysis, doi
  11. (1974). Fourier multipliers and estimates for the Fourier transform of measures carried by smooth curves in R2,
  12. (2001). Fourier restriction estimates for ane arclength measures in the plane,
  13. (1985). Fourier restriction theorems for curves with ane and Euclidean arclengths, doi
  14. (1987). Fourier restriction theorems for degenerate curves, doi
  15. (2006). Fourier restriction to convex surfaces in R3, doi
  16. Fourier restriction to polynomial curves I: A geometric inequality, doi
  17. (2003). Lp improving bounds for averages along curves,
  18. Lp-improving properties for some measures supported on curves,
  19. (2001). Mixed norm estimates for a restricted X-ray transform in R4 and R5, doi
  20. (2002). Mixed norm estimates for a restricted X-ray transform, doi
  21. Mixed norm estimates for certain generalised Radon transforms, doi
  22. (1991). Oscillatory integrals with polynomial phase, doi
  23. (2006). Quasi-extremals for a Radon-like transform, preprint,
  24. (2002). Restriction and decay for at hypersurfaces, doi
  25. (2007). Restriction for at surfaces of revolution in R3, doi
  26. Restriction of Fourier transforms to curves and related oscillatory integrals, doi
  27. (2003). The LpLq mapping properties of convolution operators with the ane arclength measure on space curves, doi
  28. (2004). Two estimates for curves in the plane,

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