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arXiv · 1607.01666

$L^p$-$L^q$ off-diagonal estimates for the Ornstein--Uhlenbeck semigroup: some positive and negative results

Alex Amenta·Jonas Teuwen
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Abstract

We investigate $L^p(\gamma)$-$L^q(\gamma)$ off-diagonal estimates for the Ornstein-Uhlenbeck semigroup $(e^{tL})_{t > 0}$. For sufficiently large $t$ (quantified in terms of $p$ and $q$) these estimates hold in an unrestricted sense, while for sufficiently small $t$ they fail when restricted to maximal admissible balls and sufficiently small annuli. Our counterexample uses Mehler kernel estimates.

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Alex Amenta, Jonas Teuwen. 2016-07-06. $L^p$-$L^q$ off-diagonal estimates for the Ornstein--Uhlenbeck semigroup: some positive and negative results. https://arxiv.org/abs/1607.01666

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