An estimation for a family of oscillatory integrals

Volume 154 / 2003

Magali Folch-Gabayet, James Wright Studia Mathematica 154 (2003), 89-97 MSC: Primary 42B15. DOI: 10.4064/sm154-1-6


Let $K$ be a Calderón–Zygmund kernel and $P$ a real polynomial defined on ${\mathbb R}^n$ with $P(0)=0$. We prove that convolution with $K \mathop {\rm exp}\nolimits (i/P) $ is continuous on $L^2 ({\mathbb R}^n)$ with bounds depending only on $K$, $n$ and the degree of $P$, but not on the coefficients of $P$.


  • Magali Folch-GabayetInstituto de Matemáticas, UNAM
    Area de la Investigación Cient{í}fica
    Circuito Exterior, Ciudad Universitaria
    México, D.F. 04510, México
  • James WrightDepartment of Mathematics and Statistics
    University of Edinburgh
    JCMB, King's Buildings
    Mayfield Road
    Edinburgh EH9 3JZ, Scotland

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