Some sharp bilinear space-time estimates for the wave equation

TL;DR

This paper establishes sharp bilinear space-time estimates for the wave equation's half-wave propagator, extending known results to radially symmetric data and a broader range of exponents.

Contribution

It introduces new sharp bilinear estimates for the wave equation, including for radially symmetric initial data beyond classical exponent ranges.

Findings

Sharp bilinear estimates for the half-wave propagator.

Extension of estimates to radially symmetric data.

Broader range of exponents for which estimates hold.

Abstract

We prove a family of sharp bilinear space-time estimates for the half-wave propagator. As a consequence, for radially symmetric initial data, we establish sharp estimates of this kind for a range of exponents beyond the classical range.