半调和性、积分平均与Euler型向量场
Semi-harmonicity, Integral Means and Euler Type Vector Fields
摘要：
引入半Riemann域上函数的Dirichlet积和广义Euler向量场，包括径向场、$\bar \partial$ -Euler场和$\bar \partial$ -Neumann向量场.研究了黎曼域上函数的积分平均和调和留数。引入复空间上函数的半调和性概念。证明了在Riemann域上，局部向前$L^2$ -函数的半调和性不仅具有弱调和性，而且具有局部均值性质.特别地，Weyl引理被推广到Riemann域。
英文摘要：
The Dirichlet product of functions on a semi-Riemann domain and generalized Euler vector fields, which include the radial, $\bar \partial$-Euler, and the $\bar \partial$-Neumann vector fields, are introduced. The integral means and the harmonic residues of functions on a Riemann domain are studied. The notion of semi-harmonicity of functions on a complex space is introduced. It is shown that, on a Riemann domain, the semi-harmonicity of a locally forwardly $L^2$-function is characterized by local mean-value properties as well as by weak-harmonicity. In particular, the Weyl's Lemma is extended to a Riemann domain.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
