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

2018/02/07 by Bañuelos, Rodrigo, Baudoin, Fabrice, Chen, Li
#FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.1802.02410

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, SU(2), and Riesz transforms on forms and spinors.

Related

• Martingale transforms and their projection operators on manifolds
• Sharp martingale inequalities and applications to Riesz transforms on manifolds, Lie groups and Gauss space
• Martingale transform and Lévy Processes on Lie Groups
• On the L^p-estimates of Riesz transforms on forms over complete Riemanian manifolds
• On the L^p-estimates for Beurling-Ahlfors and Riesz transforms on Riemannian manifolds