We study properties of \(\mathcal {A}\)-harmonic and \(\mathcal {A}\)-superharmonic functions involving an operator having generalized Orlicz growth. Our framework embraces reflexive Orlicz spaces, as well as natural variants of variable exponent and double-phase spaces. In particular, Harnack’s Principle and Minimum Principle are provided for \(\mathcal {A}\)-superharmonic functions.

中文翻译：

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具有强非线性算子的广义超谐函数

我们研究涉及算子具有广义Orlicz增长的\（\ mathcal {A} \）-调和和\（\ mathcal {A} \）-超调和函数的性质。我们的框架包含自反Orlicz空间，以及可变指数和双相空间的自然变体。特别地，为\（\ mathcal {A} \）-超谐波函数提供了Harnack原理和最小原理。