论文标题

Lévy发电机的Liouville定理

A Liouville theorem for Lévy generators

论文作者

Kühn, Franziska

论文摘要

在温和的假设下,我们为“ laplace”方程式$ au = 0 $建立了与无穷小发电机$ a $ a $相关的“ laplace”等式的liouville定理:如果$ u $是$ au = 0 $的薄弱解决方案,那么在大多数(合适的)多项式增长中,那么$ u $ u $ us $ u $是多项式。作为副产品,我们获得了与Lévy过程相关的半群的新规律性估计。

Under mild assumptions, we establish a Liouville theorem for the "Laplace" equation $Au=0$ associated with the infinitesimal generator $A$ of a Lévy process: If $u$ is a weak solution to $Au=0$ which is at most of (suitable) polynomial growth, then $u$ is a polynomial. As a by-product, we obtain new regularity estimates for semigroups associated with Lévy processes.

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