Geometric & Functional Analysis GAFA

, Volume 16, Issue 1, pp 126–163

A geometric approach to the Littlewood–Paley theory

Original Paper

DOI: 10.1007/s00039-006-0551-1

Cite this article as:
Klainerman, S. & Rodnianski, I. GAFA, Geom. funct. anal. (2006) 16: 126. doi:10.1007/s00039-006-0551-1

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 with the work of the authors on the geometry of null hypersurfaces with a finite curvature flux condition, see [KR1,2]. We are confident however that it can be applied, and extended, to many different situations.

Keywords and phrases.

Heat flow for tensorsparaproductsBochner identity

2000 Mathematics Subject Classification.

35J10

Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA