Weak $(1,1)$ Boundedness of Riesz Transforms on Vector Bundles

Abstract

The weak $(1,1)$ boundedness of (local) Riesz transforms corresponding to a large class of Schrödinger operators on vector bundles is proved, mainly assuming the generalized volume doubling condition, either Gaussian or sub-Gaussian upper bounds for the heat kernel only in short time, and derivative estimates of Bismut type for the corresponding semigroup.

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