We obtain a pointwise description of functions belonging to function spaces with the lattice property. In particular, it is valid for Banach function spaces provided that the Hardy–Littlewood maximal operator is bounded. We also study weighted grand Sobolev spaces, defined on arbitrary open sets $\Omega$ (of finite or infinite measure) in ${\mathbb{R}}^n$, and provide pointwise description of them.

中文翻译：

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关于大Sobolev空间和Banach函数空间的逐点描述

我们获得具有点阵属性的函数空间的逐点描述。特别是，如果Hardy–Littlewood极大算子是有界的，它对Banach函数空间是有效的。我们还研究了在任意开放集上定义的加权大Sobolev空间$\Omega$ （有限或无限量）在 ${\mathbb{[R}}^{ñ}$，并提供它们的逐点描述。