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.

Other Information: 

DG-MP-PDE Seminar 2006