We derive necessary and sufficient conditions on weights guaranteeing the one-weight Sobolev-type inequality for strong fractional maximal and multiple fractional integral operators in grand mixed norm Lebesgue spaces. As a consequence, appropriate statements for fractional integral operators defined on regular curves and domains in \({{\mathbb {R}}}^n\) are obtained.

中文翻译：

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盛大混合范数Lebesgue空间中的加权Sobolev不等式

我们推导了保证混合范数Lebesgue空间中强分数最大和多重分数积分算子的一重Sobolev型不等式的权重的充要条件。结果，获得了在\（{{\ mathbb {R}}} ^ n \）中的规则曲线和域上定义的分数积分算子的适当陈述。