论文标题
Lévy发电机的Liouville定理
A Liouville theorem for Lévy generators
论文作者
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.
