Derivative estimates of semigroups and Riesz transforms on vector bundles
by Anton Thalmaier and Feng-Yu Wang
We use versions of Bismut type derivative formulas obtained
by Driver-Thalmaier (2001), 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.
Potential Analysis 20 (2004) 105-123
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