Some sharp $L^2 \to L^p$ decay estimates for $(2+1)$-dimensional degenerate oscillatory integral operators

TL;DR

This paper derives sharp decay estimates for certain 2+1 dimensional oscillatory integral operators with polynomial phases, using Stein's complex interpolation method.

Contribution

It introduces new sharp $L^2 o L^p$ decay estimates for degenerate oscillatory integrals in 2+1 dimensions, expanding understanding of their behavior.

Findings

Established sharp $L^2 o L^p$ decay bounds.

Applied Stein's complex interpolation to polynomial phase operators.

Enhanced theoretical framework for oscillatory integral estimates.

Abstract

We investigate $(2+1)-$dimensional oscillatory integral operators characterized by polynomial phase functions. By employing Stein's complex interpolation, we derive sharp $L^2\to L^p$ decay estimates for these operators.