We prove a Julia inequality for bounded non-commutative functions on polynomial polyhedra. We use this to deduce a Julia inequality for holomorphicfunctions on classical domains in $$\mathbb {C}^d$$Cd. We look at differentiability at a boundary point for functions that have a certain regularity there.

中文翻译：

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一个非交换的 Julia 不等式

我们证明了多项式多面体上有界非交换函数的 Julia 不等式。我们用它来推导出 $$\mathbb {C}^d$$Cd 中经典域上全纯函数的 Julia 不等式。我们查看在边界点处具有一定规律性的函数的可微性。