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Gundy-Varopoulos martingale transforms and their projection operators on manifolds and vector bundles
Rodrigo Bañuelos, Fabrice Baudoin, Li Chen · 2018-02-07 · via math.PR updates on arXiv.org

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.

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