title: Estimates for a class of oscillatory integrals and decay rates for wave-type equations.
abstract: This paper investigates higher order wave-type equations of the form [Formula: see text], where the symbol [Formula: see text] is a real, non-degenerate elliptic polynomial of the order [Formula: see text] on [Formula: see text]. 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) [Formula: see text] estimates on the wave solution in terms of the initial conditions.
authors.affiliation: Institut für Analysis und Scientific Computing, Technische Universität Wien, Wiedner Hauptstr. 8, A-1040 Wien, Austria.
authors.forename: Anton
authors.initials: A
authors.lastname: Arnold
authors.forename: Jinmyong
authors.initials: J
authors.lastname: Kim
authors.forename: Xiaohua
authors.initials: X
authors.lastname: Yao
keywords: Fundamental solution estimate; Higher-order wave equation; Oscillatory integral