The purpose of this paper is three-fold: the first is to determine the Campanato-Sobolev space $I_N({\mathcal{L}}^{p,\kappa })$ by means of ${\sum }_{|\alpha |=N}{\Vert D^{\alpha }f\Vert }_{{\mathcal{L}}^{p,\kappa }}$ - the sum of the Campanato norms of the derivatives $D^{\alpha }f$ with $|\alpha |=N$; the second is to characterize Morrey's fractional integrals $\{Tf:f\in L^{p,\kappa }\}$ in the Campanato-Sobolev space $I_s({\mathcal{L}}^{p,\kappa })$; the third is to find a distributional solution $F\in {({\mathcal{L}}^{q,\lambda })}^n$ of the mean curvature type divergence equation $\mathrm{div}F=f\in L^{p,\kappa }$ (the Morrey space). And yet, the here-established three theorems and their proofs are not only novel but also nontrivial.

中文翻译：

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坎帕纳托-索伯列夫空间和div F  =  f中的莫里分数积分

本文的目的是三个方面：首先是确定Campanato-Sobolev空间 ${\mathrm{一世}}_{ñ}（{\mathcal{大号}}^{p，\kappa }）$ 通过 ${\sum }_{|\alpha |=ñ}{\Vert d^{\alpha }F\Vert }_{{\mathcal{大号}}^{p，\kappa }}$ -衍生品的Campanato规范的总和 $d^{\alpha }F$ 与 $|\alpha |=ñ$; 第二个是刻画Morrey的分数积分$\{ŤF：F\in {\mathrm{大号}}^{p，\kappa }\}$ 在Campanato-Sobolev空间 ${\mathrm{一世}}_s（{\mathcal{大号}}^{p，\kappa }）$; 第三是找到分配解决方案$F\in {（{\mathcal{大号}}^{q，\lambda }）}^{ñ}$ 平均曲率类型散度方程 $\mathrm{div}F=F\in {\mathrm{大号}}^{p，\kappa }$（莫里空间）。但是，这里建立的三个定理及其证明不仅新颖，而且意义非凡。