Non-Interpolation: Result for Nonlinear Mappings Between Sobolev Spaces

摘要

The conditions for nonlinear mappings between Sobolev spaces are given. Mappings will be bounded if f is a polynomial of prescribed maximal degree, e.g., only if f is linear. Such results provide non-interpolation theorems for these mappings and so for example severly limits the application of certain techniques used in the study of global existence of smooth solutions to nonlinear wave and Schroedinger equations. These results are extended to a class of nonlocalized mappings of Hartree-type.