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Estimates of hyperbolic equations in Hardy spaces

✍ Scribed by Der–Chen Chang; Yong–Seok Lee

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
329 KB
Volume
254-255
Category
Article
ISSN
0025-584X

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✦ Synopsis

The aim of this paper is to study estimates of hyperbolic equations in Hardy classes. Consider the Cauchy problem P (Dt, Dx)u(t, x) = 0 for x ∈ R d and t > 0 with the initial conditions D j t u(0, x) = gj (x), j = 0, 1, . . . , m -1. We assume that the symbol P(τ, ξ) of P (Dt, Dx) can be factorized as

Here n = max{n1, . . . , nm}. In particular, P (Dt, Dx)u = ∂ 2 u ∂t 2 -∆u = 0 with u(0, x) = f (x) and ∂u ∂t (0, x) = g(x), then the solution u of the wave equation is in

p -1 2 and 0 < p < ∞.

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