发表机构
Università degli Studi di Padova; University of Gothenburg; Chalmers University of Technology（帕多瓦大学; 哥德堡大学; 查尔姆斯理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对一般非对称Ornstein-Uhlenbeck半群，证明了跳跃拟半范数的L^p界和弱型(1,1)振荡不等式，通过分解半群成分明确有界与无界部分。
AI 中文摘要
我们考虑一个一般的、非对称的Ornstein--Uhlenbeck半群$(\mathcal H_t)_{t>0}$。我们证明了对于$1 < p < \infty$，跳跃拟半范数的$L^p$界，以及一个弱型(1,1)振荡不等式，两者均关于不变测度。这些结果是在阶$\varrho=2$的情况下建立的。为此，我们分析$(\mathcal H_t)_{t>0}$的具体组成部分，通过区分$t$的小值和大值，以及局部和全局空间区域。这种分解使我们能够明确识别半群的哪些部分保持有界，哪些部分导致有界性的失败，无论是在弱意义还是强意义下，甚至关于Lebesgue测度也是如此。
英文摘要
We consider a general, nonsymmetric Ornstein--Uhlenbeck semigroup $(\mathcal H_t)_{t>0}$. We prove an $L^p$ bound for the jump quasi-seminorms for $1 < p < \infty$ and a weak type (1,1) oscillation inequality, both with respect to the invariant measure. These results are established for the order $\varrho=2$. To do so, we analyze specific components of $(\mathcal H_t)_{t>0}$, by distinguishing between small and large values of $t$, and between local and global spatial zones. This decomposition allows us to explicitly identify which parts of the semigroup remain bounded and which are responsible for the failure of boundedness, both in a weak and in a strong sense, even with respect to Lebesgue measure.
Comments28 pages
