Lp-Lq Local Smoothing Estimates for the Wave Equation via k-Broad Fourier Restriction.

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 R n × R for all n ≥ 3 via a Bourgain–Guth broad-narrow analysis. An interesting feature is that local smoothing estimates for e i t - Δ are not invariant under Lorentz rescaling. [ABSTRACT FROM AUTHOR]