Articoli correlati a Lectures on Analysis on Metric Spaces
Sinossi
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.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Contenuti
1. Covering Theorems.- 2. Maximal Functions.- 3. Sobolev Spaces.- 4. Poincaré Inequality.- 5. Sobolev Spaces on Metric Spaces.- 6. Lipschitz Functions.- 7. Modulus of a Curve Family, Capacity, and Upper Gradients.- 8. Loewner Spaces.- 9. Loewner Spaces and Poincaré Inequalities.- 10. Quasisymmetric Maps: Basic Theory I.- 11. Quasisymmetric Maps: Basic Theory II.- 12. Quasisymmetric Embeddings of Metric Spaces in Euclidean Space.- 13. Existence of Doubling Measures.- 14. Doubling Measures and Quasisymmetric Maps.- 15. Conformal Gauges.- References.
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Lectures on Analysis on Metric
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Lectures on Analysis on Metric Spaces (Universitext)
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Lectures on analysis on metric spaces Juha Heinonen. Universitext.
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Lectures on analysis on metric spaces.
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Hardcover. Condizione: new. Hardcover. 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. Recent developments in complex analysis have permitted researchers to replace Euclidean spaces by general metric spaces. The author is a great expositor and gives a first taste of this exciting new area. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9780387951041
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Lectures on Analysis on Metric Spaces (Universitext)
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Lectures on Analysis on Metric Spaces (Universitext)
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