Wolff's inequality for hypersurfaces

• Autores: Malabika Pramanik, Izabella Laba
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 57, Fasc. Extra 1, 2006 (Ejemplar dedicado a: Proceedings of the 7th International Conference on Harmonic Analysis and Partial Differential Equations), págs. 293-326
• Idioma: español
• Enlaces
  • Texto completo
• Resumen

  • We extend Wol ¿s ¿local smoothing¿ inequality [19] to a wider class of not necessarily conical hypersurfaces of codimension 1. This class includes surfaces with nonvanishing curvature, as well as certain surfaces with more than one flat direction. An immediate consequence is the Lp-boundedness of the corresponding Fourier multiplier operators.

• Referencias bibliográficas
  • D. Békollé, A. Bonami, G. Garrigós, and F. Ricci, Littlewood-Paley decompositions related to symmetric cones and Bergman projections in tube...
  • J. Bourgain, Estimates for cone multipliers, Oper. Theory Adv. Appl. 77 (1995), 41–60.
  • L. Carleson and P. Sjölin, Oscillatory integrals and a multiplier problem for the disc, Studia Math. 44 (1972), 287–299.
  • C. Fefferman, A note on spherical summation multipliers, Israel J. Math. 15 (1973), 44–52.
  • L. Hörmander, Oscillatory integrals and multipliers on $FL^p$, Ark. Mat. 11 (1973), 1–11.
  • I. Laba and T. Wolff, A local smoothing estimate in higher dimensions, J. Anal. Math. 88 (2002), 149–171.
  • S. Lee, Improved bounds for Bochner-Riesz and maximal Bochner-Riesz operators, Duke Math. J. 122 (2004), 205–232.
  • J.M. Marstrand, Packing circles in the plane, Proc. London Math. Soc. 55 (1987), 37–58.
  • G. Mockenhaupt, A. Seeger, and C. Sogge, Wave front sets, local smoothing and Bourgain’s circular maximal theorem, Ann. of Math. (2) 134 (1992),...
  • M. Pramanik and A. Seeger, Averages over curves in $\mathbb{R}^3$ and associated maximal operators. To appear in Amer. J. Math.
  • W. Schlag, A generalization of Bourgain’s circular maximal theorem, J. Amer. Math. Soc. 10 (1997), 103–122.
  • E.M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, NJ,...
  • T. Tao, Recent progress on the restriction conjecture, Park City proceedings, to appear.
  • T. Tao and A. Vargas, A bilinear approach to cone multipliers, I and II, Geom. Funct. Anal. 10 (2000), 185–215 and 216–258.
  • T. Wolff, A Kakeya-type problem for circles, Amer. J. Math. 119 (1997), 985–1026.
  • T. Wolff, Recent work connected with the Kakeya problem, Prospects in Mathematics (Princeton, NJ, 1996), 129–162, Amer. Math. Soc., Providence,...
  • T. Wolff, An improved bound for Kakeya type maximal functions, Rev. Mat. Iberoamericana 11 (1995), 651–674.
  • T. Wolff, A sharp bilinear cone restriction estimate, Ann. of Math. (2) 153 (2001), 661–698.
  • T. Wolff, Local smoothing type estimates on $L^p$ for large $p$, Geom. Funct. Anal. 10 (2000), 1237–1288.