We give a review of the development of microlocal defect functionals and explain a connection between two recent notions in the field: the H-distributions and the microlocal compactness forms. We also provide a simplified approach to the concept of microlocal compactness forms, generalise them to a fractional setting, and connect this variant to H-distributions and Young measures.

中文翻译：

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关于H分布与微观局部紧致形式之间的关系

我们对微局部缺陷功能的发展进行了回顾，并解释了该领域中两个最新概念之间的联系：H分布和微局部致密性形式。我们还为微局部紧致形式的概念提供了一种简化方法，将它们推广为分数设置，并将此变量与H分布和Young度量联系起来。