Abstract D. Adams type trace inequalities for multiple fractional integral operators in grand Lebesgue spaces with mixed norms are established. Operators under consideration contain multiple fractional integrals defined on the product of quasi-metric measure spaces, and one-sided multiple potentials. In the case when we deal with operators defined on bounded sets, the established conditions are simultaneously necessary and sufficient for appropriate trace inequalities. The derived results are new even for multiple Riesz potential operators defined on the product of Euclidean spaces.

中文翻译：

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混合范数大勒贝格空间中分数积分的迹不等式

摘要 D. 建立了具有混合范数的大 Lebesgue 空间中多个分数积分算子的 Adams 型迹不等式。所考虑的算子包含定义在拟度量空间和单边多势的乘积上的多个分数积分。在我们处理定义在有界集合上的算子的情况下，既定条件对于适当的迹不等式来说同时是必要和充分的。即使对于定义在欧几里德空间乘积上的多个 Riesz 势算子，导出的结果也是新的。