## L^2 decay estimates for oscillatory integral operators in several variables with homogeneous polynomial phases

- Date: 11/28/2006

Malabika Pramanik (University of British Columbia)

University of British Columbia

Oscillatory integral operators mapping $L^2(mathbb R^{n_1})$ to

$L^2(mathbb R^{n_2})$ play an important role in many problems in

harmonic analysis and partial differential equations. We will briefly

discuss the applicability of these operators in various contexts and

give an overview of the current literature. We also mention recent

results (joint with Allan Greenleaf and Wan Tang) where, extending

earlier work of Phong and Stein in the case $n_1 = n_2 = 1$, we obtain

optimal decay rates for the $L^2$ operator norm of oscillatory integral

operators in $2+2$ variables with generic phases. Some other higher

dimensional situations are also addressed.

DG-MP-PDE Seminar 2006