Sharp $L^p$-Boundedness of Oscillatory Integral Operators with Polynomial Phases

Abstract

In this paper, we shall prove the $L^p$ endpoint decay estimates of oscillatory integral operators with homogeneous polynomial phases $S$ in $\mathbb{R}\times \mathbb{R}$. As a consequence, sharp $L^p$ decay estimates are also obtained when polynomial phases have the form $S(x^{m_1},y^{m_2})$ with $m_1$ and $m_2$ being positive integers.

27 pages

Cited by in corpus (1)

• The sharp $L^p$ decay of oscillatory integral operators with certain homogeneous polynomial phases in several variables