论文标题
离散对称平均运算符的liouville定理
The Liouville theorem for discrete symmetric averaging operators
论文作者
论文摘要
我们在晶格上介绍平均运算符$ \ Mathbb {z}^d $，并研究Liouville属性，以满足与此类运营商相关的平均值属性的功能。该框架包含离散的谐波，$ p $ -Harmonic，$ \ infty $ -Harmonic和所谓的游戏$ p $ harmonic函数。我们的方法提供了$ \ mathbb {z}^d $上的正$ p $ harmonic函数的liouville定理的基本替代证明。
We introduce averaging operators on lattices $\mathbb{Z}^d$ and study the Liouville property for functions satisfying mean value properties associated to such operators. This framework encloses discrete harmonic, $p$-harmonic, $\infty$-harmonic and the so-called game $p$-harmonic functions. Our approach provides an elementary alternative proof of the Liouville Theorem for positive $p$-harmonic functions on $\mathbb{Z}^d$.
