Optimal angle of the holomorphic functional calculus for the classical Ornstein-Uhlenbeck operator on $L^p$

Sean Harris

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arXiv · 1812.08300

Optimal angle of the holomorphic functional calculus for the classical Ornstein-Uhlenbeck operator on $L^p$

Sean Harris

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Abstract

We give a simple proof of the fact that the classical Ornstein-Uhlenbeck operator $L$ is R-sectorial of angle $arcsin|1-2/p|$ on $L^{p}(\mathbb{R}^{n},\exp(-|x|^2/2)dx)$ (for $1<p<\infty$). Applying the abstract holomorphic functional calculus theory of Kalton and Weis, this immediately gives a new proof of the fact that $L$ has a bounded $H^{\infty}$ functional calculus with this optimal angle.

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BibTeX RIS

Sean Harris. 2018-12-20. Optimal angle of the holomorphic functional calculus for the classical Ornstein-Uhlenbeck operator on $L^p$. https://arxiv.org/abs/1812.08300

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