Estimates for Hyperbolic Equations of Space Dimension 3 |
| |
Authors: | Mitsuru Sugimoto |
| |
Institution: | Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560, Japan |
| |
Abstract: | We discuss the problem of boundedness fromLp(Rn) toLp′(Rn) (1/p+1/p′=1, 1?p?2) of operators of the typeM=F−1ei?(ξ)a(ξ) F, which is related to the study of hyperbolic equations with constant coefficients. The boundedness is dependent on a geometrical property ofΣ=?−1(1), and its dependence has been exactly determined in the casesn=2, 1?p?2 andn?3,p=1, 2 (M. Sugimoto,Math. Z.215(1994), 519–531;222(1996), 521–531). This paper is devoted to the unsolved case 1<p<2, and a strange phenomenon is exhibited in the simplest casen=3. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|