Estimates for hyperbolic equations of space dimension 3 (Q1279641)

The author discussed the problem of boundedness from \(L^p(\mathbb{R}^n)\) to \(L^{p'}(\mathbb{R}^n)\) (\(\frac 1p +\frac 1{p'}=1, 1\leq p\leq 2\)) of operators of the type \(M=F^{-1}e^{i\phi(\xi)}F\), which is related to the study of the \(L^p\)-\(L^{p'}\) estimates of the solution of hyperbolic equations with constant coefficients. The author mainly considered the case \(1<p<2\), \(n=3\) in this paper. The result is a supplement of his previous works for other cases for \(p\) and \(n\).