Improved local smoothing estimate for the wave equation in higher dimensions

Abstract

In this paper, we establish the sharp $k$-broad estimate for a class of phase functions satisfying the homogeneous convex conditions. As an application, we obtain improved local smoothing estimates for the half-wave operator in dimensions $n\ge 3$. As a byproduct, we also generalize the restriction estimates of Ou--Wang to a broader class of phase functions.

32 pages, 3 figures, Referees' suggestions incorporated. To appear in J. Func. Anal

References in corpus (1)

• Kakeya sets of curves

Cited by in corpus (1)

• Local smoothing for the Hermite wave equation