We study spaces of Holder type functions harmonic in the unit ball and half space with some smoothness conditions up to the boundary. The first type is the Holder type space of harmonic functions with prescribed modulus of continuity ω = ω(h) and the second is the variable exponent harmonic Holder space with the continuity modulus |h|λ(·). We give a characterization of functions in these spaces in terms of the behavior of their derivatives near the boundary.

中文翻译：

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单位球和半空间中调和函数的广义 Hölder 型空间

我们研究了单位球和半空间中的 Holder 型函数空间，在边界上有一些平滑条件。第一种类型是具有规定连续模量ω = ω(h) 的调和函数的Holder 型空间，第二种是具有连续模量|h|λ(·) 的变指数调和Holder 空间。我们根据它们在边界附近的导数的行为来描述这些空间中的函数。