Estimates for a class of oscillatory integrals and decay rates for wave-type equations☆
نویسندگان
چکیده
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.
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