Lectures on Analysis on Metric Spaces
Lectures on Analysis on Metric Spaces
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DOI：
10.1007/978-1-4613-0131-8
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发表时间：
2000-12
期刊：
影响因子：
--
通讯作者：
J. Heinonen
中科院分区：
文献类型：
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作者：
J. Heinonen
在没有先验光滑结构的空间中的分析已经取得了进展，包括了一阶微积分中的概念。特别是，在理解Lipschitz函数和拟共形映射在相当一般的环境下的无穷小相对于整体行为方面已经有了重要的进展；抽象的Sobolev空间理论在这一发展中起到了重要作用。这本书的目的是交流该领域的一些最新工作，同时为读者学习更多实质性的相关文章做好准备。材料大致可以分为三种不同的类型：古典、标准但有时带有新的曲折，以及最近的。作者首先研究了度量度量空间的基本覆盖定理及其在分析中的应用。然后是关于索博列夫空间的讨论，强调在更大的背景下有效的原则。这本书的最后几节介绍了度量空间之间的拟对称映射的基本理论。许多材料都是相对较新的，是第一次以书籍的形式出现。有很多练习。这本书非常适合自学，或者作为研究生课程或研讨会的课本。该材质适用于对非平滑设置中的分析和几何图形感兴趣的任何人。
Analysis in spaces with no a priori smooth structure has progressed to include concepts from the first order calculus. In particular, there have been important advances in understanding the infinitesimal versus global behavior of Lipschitz functions and quasiconformal mappings in rather general settings; abstract Sobolev space theories have been instrumental in this development. The purpose of this book is to communicate some of the recent work in the area while preparing the reader to study more substantial, related articles. The material can be roughly divided into three different types: classical, standard but sometimes with a new twist, and recent. The author first studies basic covering theorems and their applications to analysis in metric measure spaces. This is followed by a discussion on Sobolev spaces emphasizing principles that are valid in larger contexts. The last few sections of the book present a basic theory of quasisymmetric maps between metric spaces. Much of the material is relatively recent and appears for the first time in book format. There are plenty of exercises. The book is well suited for self-study, or as a text in a graduate course or seminar. The material is relevant to anyone who is interested in analysis and geometry in nonsmooth settings.