An estimation for a family of oscillatory integrals
Volume 154 / 2003
Studia Mathematica 154 (2003), 89-97
MSC: Primary 42B15.
DOI: 10.4064/sm154-1-6
Abstract
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 $P$.
