This paper investigates higher order wave-type equations of the form partial derivative(u)u + P(D-x)u = 0, where the symbol P(xi) is a real, non-degenerate elliptic polynomial of the order m >= 4 on R-n. Using methods from harmonic analysis, we first establish global pointwise time-space estimates for a class of oscillatory integrals that appear as the fundamental solutions to the Cauchy problem of such wave equations. These estimates are then used to establish (pointwise-in-time) L-p-L-q estimates on the wave solution M terms ...
