Gundy–Varopoulos martingale transforms and their projection operators on manifolds and vector bundles

This paper proves the L p boundedness of generalized first order Riesz transforms obtained as conditional expectations of martingale transforms à la Gundy–Varopoulos for quite general diffusions on manifolds and vector bundles. Several specific examples and applications are presented: Lie groups of...

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Bibliographic Details
Published in:Mathematische annalen 2020-10, Vol.378 (1-2), p.359-388
Main Authors: Bañuelos, Rodrigo, Baudoin, Fabrice, Chen, Li
Format: Article
Language:English
Subjects:
Bundles
Lie groups
Manifolds
Martingales
Mathematics
Mathematics and Statistics
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Summary:This paper proves the L p boundedness of generalized first order Riesz transforms obtained as conditional expectations of martingale transforms à la Gundy–Varopoulos for quite general diffusions on manifolds and vector bundles. Several specific examples and applications are presented: Lie groups of compact type, the Heisenberg group, SU ( 2 ) , and Riesz transforms on forms and spinors.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-019-01825-4