Let $A$ be an expansive dilation on $\mathbb{R}^{n}$ and $\unicode[STIX]{x1D711}:\mathbb{R}^{n}\times [0,\infty )\rightarrow [0,\infty )$ an anisotropic growth function. In this article, the authors introduce the anisotropic weak Musielak–Orlicz Hardy space $\mathit{WH}_{A}^{\unicode[STIX]{x1D711}}(\mathbb{R}^{n})$ via the nontangential grand maximal function and then obtain its Littlewood–Paley characterizations in terms of the anisotropic Lusin-area function, $g$-function or $g_{\unicode[STIX]{x1D706}}^{\ast }$-function, respectively. All these characterizations for anisotropic weak Hardy spaces $\mathit{WH}_{A}^{p}(\mathbb{R}^{n})$ (namely, $\unicode[STIX]{x1D711}(x,t):=t^{p}$ for all $t\in [0,\infty )$ and $x\in \mathbb{R}^{n}$ with $p\in (0,1]$) are new. Moreover, the range of $\unicode[STIX]{x1D706}$ in the anisotropic $g_{\unicode[STIX]{x1D706}}^{\ast }$-function characterization of $\mathit{WH}_{A}^{\unicode[STIX]{x1D711}}(\mathbb{R}^{n})$ coincides with the best known range of the $g_{\unicode[STIX]{x1D706}}^{\ast }$-function characterization of classical Hardy space $H^{p}(\mathbb{R}^{n})$ or its weighted variants, where $p\in (0,1]$.

中文翻译：

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各向异性弱 MUSIELAK-ORLICZ 哈代空间的利特伍德-帕利表征

让$澳元是一个膨胀的扩张$\mathbb{R}^{n}$和$\unicode[STIX]{x1D711}:\mathbb{R}^{n}\times [0,\infty )\rightarrow [0,\infty )$各向异性生长函数。在本文中，作者介绍了各向异性的弱 Musielak-Orlicz Hardy 空间$\mathit{WH}_{A}^{\unicode[STIX]{x1D711}}(\mathbb{R}^{n})$通过非切线大极大函数，然后根据各向异性 Lusin 面积函数获得其 Littlewood-Paley 表征，$g$-函数或$g_{\unicode[STIX]{x1D706}}^{\ast }$-函数，分别。各向异性弱哈代空间的所有这些表征$\mathit{WH}_{A}^{p}(\mathbb{R}^{n})$（即，$\unicode[STIX]{x1D711}(x,t):=t^{p}$对所有人$t\in [0,\infty)$和$x\in \mathbb{R}^{n}$和$p\in (0,1]$) 是新的。此外，范围$\unicode[STIX]{x1D706}$在各向异性$g_{\unicode[STIX]{x1D706}}^{\ast }$- 功能表征$\mathit{WH}_{A}^{\unicode[STIX]{x1D711}}(\mathbb{R}^{n})$与最知名的范围相吻合$g_{\unicode[STIX]{x1D706}}^{\ast }$-经典哈代空间的函数表征$H^{p}(\mathbb{R}^{n})$或其加权变体，其中$p\in (0,1]$.