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

  • Rodrigo Bañuelos
  • Fabrice BaudoinEmail author
  • Li Chen
Article
  • 35 Downloads

Abstract

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, \(\mathbb {SU}(2)\), and Riesz transforms on forms and spinors.

Notes

Acknowledgements

We would like to thank the anonymous referee for the useful comments which allowed us to improve the manuscript.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA
  2. 2.Department of MathematicsUniversity of ConnecticutStorrsUSA

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