Morrey spaces are the powerful tool for the study of partial differential equations. Recently, weak Morrey spaces and weak Herz spaces are known to be useful for the study of Navier–Stokes equations. In this paper we introduce weak central Herz–Morrey spaces $W\mathcal H^{p(\cdot),q,\omega}(\mathbf B)$ and establish the weak estimate for the maximal and Riesz potential operators in the central Herz–Morrey space $\mathcal H^{p(\cdot),q,\omega}(\mathbf B)$. We also treat generalized Riesz potential operators. Further we obtain the strong estimate for Sobolev functions.

中文翻译：

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单位球上中心Herz-Morrey空间中最大和Riesz势算子的弱估计

Morrey空间是研究偏微分方程的有力工具。最近，已知弱的Morrey空间和弱的Herz空间可用于研究Navier–Stokes方程。在本文中，我们引入了弱中心Herz-Morrey空间$ W \ mathcal H ^ {p（\ cdot），q，\ omega}（\ mathbf B）$并建立了中心的最大和Riesz势算子的弱估计Herz–Morrey空间$ \数学H ^ {p（\ cdot），q，\ omega}（\ mathbf B）$。我们还对待广义Riesz潜在算子。此外，我们获得了Sobolev函数的强大估计。