Abstract
We use versions of Bismut type derivative formulas obtained by Driver and Thalmaier [9], to prove derivative estimates for various heat semigroups on Riemannian vector bundles. As an application, the weak (1,1) property for a class of Riesz transforms on a vector bundle is established. Some concrete examples of vector bundles (e.g., differential forms) are considered to illustrate the results.
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Thalmaier, A., Wang, FY. Derivative Estimates of Semigroups and Riesz Transforms on Vector Bundles. Potential Analysis 20, 105–123 (2004). https://doi.org/10.1023/A:1026310604320
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DOI: https://doi.org/10.1023/A:1026310604320