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Sub-Gaussian heat kernel estimates and quasi Riesz transforms for $1\leq p\leq 2$ (1401.2279v2)

Published 10 Jan 2014 in math.AP and math.CA

Abstract: On a complete non-compact Riemannian manifold $M$, we prove that a so-called quasi Riesz transform is always $L^p$ bounded for $1<p\leq 2$. If $M$ satisfies the doubling volume property and the sub-Gaussian heat kernel estimate, we prove that the quasi Riesz transform is also of weak type $(1,1)$.