Sobolev wavefront sets and 2-microlocal spaces play a key role in describing and analyzing the singularities of distributions in microlocal analysis and solutions of partial differential equations. Employing the continuous shearlet transform to Sobolev spaces, in this paper we characterize the microlocal Sobolev wavefront sets, the 2-microlocal spaces, and local Hölder spaces of distributions/functions. We then establish the connections among Sobolev wavefront sets, 2-microlocal spaces, and local Hölder spaces through the continuous shearlet transform.

中文翻译：

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Soarlev波前集的微局部分析和使用Shearlets的表征

Sobolev波前集和2个微局部空间在描述和分析微局部分析中的分布奇异性和偏微分方程的解中起着关键作用。利用对Sobolev空间的连续剪切波变换，在本文中，我们对分布/函数的微局部Sobolev波前集，2-微局部空间和局部Hölder空间进行了表征。然后，我们通过连续小波变换在Sobolev波前集，2-微局部空间和局部Hölder空间之间建立连接。