Abstract
We prove the boundedness on L p, 1 < p < ∞, of operators on manifolds which arise by taking conditional expectation of transformations of stochastic integrals. These operators include various classical operators such as second order Riesz transforms and operators of Laplace transform-type.
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R. Bañuelos was supported in part by NSF Grant #0603701-DMS.
F. Baudoin was supported in part by NSF Grant 0907326–DMS.
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Bañuelos, R., Baudoin, F. Martingale Transforms and Their Projection Operators on Manifolds. Potential Anal 38, 1071–1089 (2013). https://doi.org/10.1007/s11118-012-9307-8
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DOI: https://doi.org/10.1007/s11118-012-9307-8
Keywords
- Martingale transforms
- Second order Riesz transforms
- Burkholder–Davis–Gundy inequality
- Laplace type multiplier
- Schrodinger operators on manifolds