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Estimates for Solutions of Wave Equations with Vanishing Curvature

Published online by Cambridge University Press:  20 November 2018

Bernard Marshall
Bernard Marshall*
Affiliation:
McGill University, Montreal, Quebec
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 37 , Issue 6 , 01 December 1985 , pp. 1176 - 1200
Copyright
Copyright © Canadian Mathematical Society 1985

References

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