论文标题
关于与Quaternionic $ m $ -subharmonic函数相关的Quaternionic多能理论
On quaternionic pluripotential theory associated to quaternionic $m$-subharmonic functions
论文作者
论文摘要
多能理论的许多方面都被推广到Quaternionic $ m $ - subharmonic函数。我们介绍了$ m $ - hessian操作员的概念的Quaternionic版本，$ m $ - subharmonic函数，$ m $ - hessian Measure，$ m $ -capapcity，相对$ m $ m $ -Extremal函数和$ m $ $ -M $ -LELLONG数字，并根据$ d_0 $ $ $ d_1 $ $ d_1 $ $ d_1 $ $ d_1 $ $ d_1 $ $ d_1 $ $ d_1 $ d_1 $ d_1 $ d_1 $ d_1和$ \ Overline {\ partial} $，以及Quaternionic封闭的位置电流。 Quaternionic $ m $ -Hessian运算符的定义可以扩展到本地边界的Quaternionic $ m $ -subharmonic函数，并证明了相应的收敛定理。建立了有限的Quaternion $ m $ -subharmonic功能的比较原理和准原则。我们还找到了Quaternionic $ m $ -Hessian运营商的基本解决方案。
Many aspects of pluripotential theory are generalized to quaternionic $m$-subharmonic functions. We introduce quaternionic version of notions of the $m$-Hessian operator, $m$-subharmonic functions, $m$-Hessian measure, $m$-capapcity, the relative $m$-extremal function and the $m$-Lelong number, and show various propositions for them, based on $d_0$ and $ d_1$ operators, the quaternionic counterpart of $\partial$ and $\overline{\partial}$, and quaternionic closed positve currents. The definition of quaternionic $m$-Hessian operator can be extended to locally bounded quaternionic $m$-subharmonic functions and the corresponding convergence theorem is proved. The comparison principle and the quasicontinuity of bounded quaternionic $m$-subharmonic functions are established. We also find the fundamental solution of the quaternionic $m$-Hessian operator.
