Displaying similar documents to “Approximate isometries on bounded sets with an application to measure theory”

John-Nirenberg lemmas for a doubling measure

Daniel Aalto, Lauri Berkovits, Outi Elina Kansanen, Hong Yue (2011)

Studia Mathematica

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We study, in the context of doubling metric measure spaces, a class of BMO type functions defined by John and Nirenberg. In particular, we present a new version of the Calderón-Zygmund decomposition in metric spaces and use it to prove the corresponding John-Nirenberg inequality.

Quasisymmetry, measure and a question of Heinonen.

Stephen Semmes (1996)

Revista Matemática Iberoamericana

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In this paper we resolve in the affirmative a question of Heinonen on the absolute continuity of quasisymmetric mappings defined on subsets of Euclidean spaces. The main ingredients in the proof are extension results for quasisymmetric mappings and metric doubling measures.

Two problems on doubling measures.

Robert Kaufman, Jang-Mei Wu (1995)

Revista Matemática Iberoamericana

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Doubling measures appear in relation to quasiconformal mappings of the unit disk of the complex plane onto itself. Each such map determines a homeomorphism of the unit circle on itself, and the problem arises, which mappings f can occur as boundary mappings?