# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 34 (2005) pp.541-586

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### Abstract

The goal of the present paper is to derive $L^p-L^q$ estimates for wave equations with a bounded time dependent coefficient. A classification of the oscillating behaviour of the coefficient is given. This classification determines in an essential way the possibility of deriving $L^p-L^q$ decay estimates.

MSC(Primary) 35L15 35L05 wave equation, oscillating time dependent coefficient, WKB-representation,Fourier multipliers, Floquet's theory