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arXiv · 2406.01097

A multiplicative inequality of Riesz transform type on general Riemannian manifolds

El Maati Ouhabaz
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Abstract

Given any complete Riemannian manifold $M$, we prove that for every $p \in (1, 2]$ and every $\epsilon > 0$, $$ \| \nabla f \|_p^2 \le C_\epsilon \| \Delta^{\frac{1}{2} + \epsilon} f \|_{p}\| \Delta^{\frac{1}{2} - \epsilon} f \|_{p}.$$The estimate is dimension free. This inequality is even proved in the abstract setting of generators of sub-Markov semigroups.

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El Maati Ouhabaz. 2024-06-03. A multiplicative inequality of Riesz transform type on general Riemannian manifolds. https://arxiv.org/abs/2406.01097

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