标题： 通过球Banach函数空间对消失Campanato空间的表征及其应用 显示英文标题

标题： Characterization of Vanishing Campanato Spaces via Ball Banach Function Spaces and Its Applications

摘要： 在本文中，作者利用球Banach函数空间一般框架内定义的一种振荡类型，提供了几种消失Campanato空间的一些新特征。 这种方法甚至在消失BMO空间的特殊情况中也带来了新的见解。 该特征揭示了消失Campanato空间固有的自我改进现象。 这种方法的关键创新在于使用高阶差分来控制振荡。 作者通过卷积平滑函数来实现这种控制，而不是直接估计这些差分。 作为额外的结果，作者还根据高阶差分获得了消失Campanato空间的新特征。 最后，作者给出了几个例子，以说明这些消失Campanato空间自然出现在Morrey空间中分数积分换位子紧性的研究中。 显示英文摘要

摘要： In this article, the authors provide some new characterizations of several vanishing Campanato spaces using a type of oscillation defined within the general framework of ball Banach function spaces. This approach yields fresh insights even in the special case of the vanishing BMO space. The characterization reveals a self-improvement phenomenon inherent in vanishing Campanato spaces. A key innovation of this approach lies in using higher-order differences to dominate oscillations. Instead of directly estimating these differences, the authors achieve the domination by smoothing the function via convolution. As additional outcomes, the authors also obtain new characterizations of vanishing Campanato spaces in terms of higher-order differences. Finally, the authors present several examples to show that these vanishing Campanato spaces naturally arise in the study on the compactness of fractional integral commutators in Morrey spaces.