Perzhan, A. V. \(H_ p\)-estimates of solutions of the Cauchy problem for a second order strictly hyperbolic equation. (Russian) Zbl 0574.35055 Mat. Issled. 80, 108-115 (1985). 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 Keywords:existence; estimates; Cauchy problem PDFBibTeX XMLCite \textit{A. V. Perzhan}, Mat. Issled. 80, 108--115 (1985; Zbl 0574.35055) Full Text: EuDML