A geometric approach to the Littlewood-Paley theory

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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.

Original languageEnglish (US)
Pages (from-to)126-163
Number of pages38
JournalGeometric and Functional Analysis
Volume16
Issue number1
DOIs
StatePublished - Feb 1 2006

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology

Keywords

  • Bochner identity
  • Heat flow for tensors
  • Paraproducts

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