$L^p-L^q$ local smoothing estimates for the wave equation via $k$-broad Fourier restriction

Abstract

We explore the connection between $k$-broad Fourier restriction estimates and sharp regularity $L^p-L^q$ local smoothing estimates for the solutions of the wave equation in ${\mathbb{R}}^n\times \mathbb{R}$ for all $n\ge 3$ via a Bourgain--Guth broad-narrow analysis. An interesting feature is that local smoothing estimates for $e^{it\sqrt{-\Delta }}$ are not invariant under Lorentz rescaling.

Final version with referee's comments incorporated; to appear in J. Fourier Anal. Appl

References in corpus (1)

• Circular average relative to fractal measures