A geometric approach to the Littlewood–Paley theory
By S. Klainerman, Igor Rodnianski. 2003
68 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/7827a925f571d539786fdee0315e929df2a40fab
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In Applied Mathematics
- Philip T. Gressman
- Robert M. Strain
- Cédric Villani
- Clément Mouhot
- Yan Guo
- Jiang Xu
- Shuichi Kawashima
In Nuclear and High Energy Physics
Citations in the corpus
- Global classical solutions of the Boltzmann equation without angular cut-off (2009, methodology): “deeper geometric aspects of our nonisotropic construction (which contrasts with the approach of Klainerman and Rodnianski [36]).”