A geometric approach to the Littlewood-Paley theory
Analysis of PDEs
2016-09-07 v1 Classical Analysis and ODEs
Differential Geometry
Abstract
We develop a geometric invariant Littlewood-Paley theory for arbitrary tensors on a compact 2 dimensional manifold. We show that all the important features of the classical LP theory survive with estimates which depend only on very limited regularity assumptions on the metric. We give invariant descriptions of Sobolev and Besov spaces and prove some sharp product inequalities. This theory has being developed in connection to the work of the authors on the geometry of null hypersurfaces with a finite curvature flux condition, see \cite{KR1}, \cite{KR3}. We are confident however that it can be applied, and extended, to many different situations.
Keywords
Cite
@article{arxiv.math/0309463,
title = {A geometric approach to the Littlewood-Paley theory},
author = {Sergiu Klainerman and Igor Rodnianski},
journal= {arXiv preprint arXiv:math/0309463},
year = {2016}
}