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 compact type, the Heisenberg group, 𝕊𝕌(2) , and Riesz transforms on forms and spinors.