取值于UMD空间的Ornstein-Uhlenbeck算子的无维度角<π/2的H^∞演算
Dimension-free $H^\infty$-calculus of angle $<π/2$ for UMD-valued Ornstein--Uhlenbeck operators
浏览论文内容
中文总结 AI 辅助
本文针对取值于UMD空间的Ornstein-Uhlenbeck算子，证明其具有维度无关的严格小于π/2的H^∞演算，通过转移定理与中心极限论证完成相关估计的推导。
中文摘要 AI 辅助
设1<p<∞，X为UMD巴拿赫空间，L_d是L^p(R^d,γ_d;X)上Ornstein-Uhlenbeck半群(P_d(t))_{t≥0}的生成元。本文证明算子-L_d是R-扇形算子，具有严格小于π/2的公共角，且界与d无关。结合Hieber-Prüss转移定理与Kalton-Weis角比较，推导出算子-L_d具有严格小于π/2的公共角的有界H^∞演算，界仍与维度无关。本文先证明相应的Walsh R-解析估计，再通过中心极限论证将其转移至Ornstein-Uhlenbeck框架。
英文摘要
Let $1<p<\infty$, let $X$ be a UMD Banach space, let $1<p<\infty$, and let $L_d$ be the generator of the Ornstein--Uhlenbeck semigroup $(P_d(t))_{t\geq 0}$ on $L^p(\mathbb R^d,γ_d;X)$. We prove that the operators $-L_d$ are $R$-sectorial with a common angle strictly smaller than $π/2$ and with bounds independent of $d$. Combining this with the Hieber--Prüss transference theorem and the Kalton--Weis angle comparison, we deduce that the operators $-L_d$ admit bounded $H^\infty$-calculi of a common angle strictly smaller than $π/2$, again with dimension-free bounds. The corresponding Walsh $R$-analyticity estimates are proved first and transferred to the Ornstein--Uhlenbeck setting by a central limit argument.
发表机构
- Delft University of Technology（代尔夫特理工大学）
机构由 AI 辅助整理，请以论文原文为准。
