We introduce and study the spaces of fractionally absolutely continuous functions of two variables of any order and the fractional Sobolev type spaces of functions of two variables. Our approach is based on the Riemann-Liouville fractional integrals and derivatives. We investigate relations between these spaces as well as between the Riemann-Liouville and weak derivatives.

中文翻译：

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通过 Riemann-Liouville 导数的二变量函数的分数 Sobolev 型空间

我们介绍并研究了任意阶二变量分数绝对连续函数空间和二变量函数分数Sobolev型空间。我们的方法基于黎曼-刘维尔分数积分和导数。我们研究这些空间之间以及黎曼-刘维尔空间和弱导数之间的关系。