Non-homogeneous harmonic analysis: 16 years of development
Non-homogeneous harmonic analysis: 16 years of development
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非齐次谐波分析：16年的发展
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
V. Eiderman
中科院分区：
文献类型：
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作者：
A. Volberg;V. Eiderman
这一调查包含的结果和方法在奇异积分理论，一个理论，这已显着发展，在过去的15-20年。中心（但不是唯一）的主题文件是连接之间的分析性质的积分和运营商与卡尔德龙-Zygmund内核和几何性质的措施。历史是追溯经典的Painlevé问题描述可去除的奇异性的有界解析函数，这提供了一个强大的激励发展的这个分支的调和分析。近几十年来的进展主要是建立了一个处理非齐次测量的装置，这里对这个装置给予了很大的关注。几个悬而未决的问题，首先是在多维的情况下，其中的方法曲率的措施是不可用的。书目：128种。
This survey contains results and methods in the theory of singular integrals, a theory which has been developing dramatically in the last 15–20 years. The central (although not the only) topic of the paper is the connection between the analytic properties of integrals and operators with Calderón–Zygmund kernels and the geometric properties of the measures. The history is traced of the classical Painlevé problem of describing removable singularities of bounded analytic functions, which has provided a strong incentive for the development of this branch of harmonic analysis. The progress of recent decades has largely been based on the creation of an apparatus for dealing with non-homogeneous measures, and much attention is devoted to this apparatus here. Several open questions are stated, first and foremost in the multidimensional case, where the method of curvature of a measure is not available. Bibliography: 128 titles.