Oscillatory integrals have been an essential part of
harmonic analysis since the beginnings of the subject. There are two main types: oscillatory integrals of the first kind
and oscillatory integrals of the second kind. Oscillatory integrals of the first kind deal with a single
variable function. The Fourier Transform is a well-known example. Oscillatory integrals of the second
kind deal with functions of two variables. My research looks at the Lp boundedness
of oscillatory integrals of the second kind through an in-depth examination of two
papers “Lp Estimates for Oscillatory Integral
Operators,” a paper by Leslie C. Cheng and Yibiao Pan, and ``On a
Stopping Process of Oscillatory Integrals” by D.H. Phong and E.M. Stein.