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\(H_ p\)-estimates of solutions of the Cauchy problem for a second order strictly hyperbolic equation. (Russian) Zbl 0574.35055

The author establishes necessary and sufficient conditions for the existence of \(L_ p\) and \(H_ p\) estimates for the solution of the Cauchy problem \[ P(i(\partial /\partial t),i(\partial /\partial x))=0,\quad x\in R^ n,\quad t>0,\quad u|_{t=0}=f_ 0(x),\quad u_ t|_{t=0}=f_ 1(x),\quad x\in R^ n, \] where P(z,x) denotes a second order polynomial in z, and \(x_ 1,...,x_ n\), while \(f_ 0,f_ 1\) are given functions.
Reviewer: S.Aizicovici

MSC:

35L15 Initial value problems for second-order hyperbolic equations
35B65 Smoothness and regularity of solutions to PDEs
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