Published online by Cambridge University Press: 20 November 2018
The solution of the Cauchy problem for a hyperbolic partial differential equation leads to a linear combination of operators Tt of the form
For example, the solution of the initial value problem
is given by u(x, t) = Ttf(x) where
Peral proved in [11] that Tt is bounded from LP(Rn) to LP(Rn) if and only if
From the homogeneity, the operator norm satisfies ‖Tt‖ ≦ Ct for all t > 0.