Singular integrals and the Newton diagram

• Autores: Stephen Wainger, James Wright, Anthony Carbery
• 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. 171-194
• Idioma: español
• Enlaces
  • Texto completo
• Resumen

  • We examine several scalar oscillatory singular integrals involving a realanalytic phase function (s, t) of two real variables and illustrate how one can use the Newton diagram of  to eciently analyse these objects.

    We use these results to bound certain singular integral operators.

• Referencias bibliográficas
  • V.I. Arnold, S.M. Guseĭn-Zade, and A.N. Varčenko, Singularities of Differentiable Maps, Volume II, Birkhäuser, Boston, Inc., Boston, MA, 1988.
  • A. Carbery, S. Wainger, and J. Wright, Double Hilbert transforms along polynomial surfaces in $\mathbb{R}^3$, Duke Math. J. 101 (2000), 499–513.
  • A. Carbery, S. Wainger, and J. Wright, Triple Hilbert transforms along polynomial surfaces in $\mathbb{R}^4$, in preparation.
  • A. Carbery, S. Wainger, and J. Wright, On properties of absolutely convergent Fourier series under analytic changes of variables, in preparation.
  • M. Greenblatt, Sharp $L^2$ estimates for one-dimensional oscillatory integral operators with $C^\infty$ phase, Amer. J. Math. 127 (2005),...
  • A. Magyar, On Fourier restriction and the Newton diagram, (preprint).
  • A. Nagel, J. Vance, S. Wainger, and D. Weinberg, Hilbert transforms for convex curves, Duke Math. J. 50 (1983), 735–744.
  • S. Patel, Double Hilbert transforms, Ph.D. thesis, University of Edinburgh, 2004.
  • D.H. Phong and E.M. Stein, The Newton polyhedron and oscillatory integral operators, Acta Math. 179 (1997), 105–152.
  • M. Pramanik and C.W. Yang, Double Hilbert transform along real-analytic surfaces in $\mathbb{R}^{d+2}$, (preprint).
  • V.S. Rychkov, Sharp $L^2$ bounds for oscillatory integral operators with $C^\infty$ phases, Math. Z. 236 (2001), 461–489.
  • A. Seeger, $L^2$-estimates for a class of singular oscillatory integrals, Math. Res. Lett. 1 (1994), 65–73.
  • A. Seeger, Radon transforms and finite type conditions, J. Amer. Math. Soc. 11 (1998), 869–897.
  • E.M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, NJ,...
  • A.N. Varčenko, Newton polyhedra and estimates of oscillatory integrals, Funkcional Anal. i Priložen. 10 (1976), 13–38.