Titlebook: Lectures on Analysis on Metric Spaces; Juha Heinonen Textbook 2001 Springer Science+Business Media New York 2001 Area.Finite.Sobolev space

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Lipschitz Functions, 1 such that .for all . and . in .. Of course, there is nothing special about having the real line as a target, and in general we call a map . : . → . between metric spaces ., or . if the constant . ≥ 1 deserves to be mentioned, if condition . holds.

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Quasisymmetric Maps: Basic Theory I,176]. We use the notation . : . → . for an embedding . of a metric space . in a metric space .. Thus, note in particular that in this notation . is not supposed to be onto. Recall that an . is a map that is a homeomorphism onto its image.

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Quasisymmetric Maps: Basic Theory II,paces from this class are H?lder continuous. Quantitative bounds for the change in Hausdorff dimension then follow. As a second topic, we discuss the relationship between quasisymmetry and quasiconformality for maps between Euclidean domains. Finally, as an example, we show how quasisymmetric maps n

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Universitexthttp://image.papertrans.cn/l/image/583476.jpg

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