Displaying similar documents to “Bilipschitz mappings and strong A ∞ weights.”

Squeezing the Sierpinski sponge

Tadeusz Iwaniec, Gaven Martin (2002)

Studia Mathematica

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We give an example relating to the regularity properties of mappings with finite distortion. This example suggests conditions to be imposed on the distortion function in order to avoid "cavitation in measure".

When is the Haar measure a Pietsch measure for nonlinear mappings?

Geraldo Botelho, Daniel Pellegrino, Pilar Rueda, Joedson Santos, Juan Benigno Seoane-Sepúlveda (2012)

Studia Mathematica

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We show that, as in the linear case, the normalized Haar measure on a compact topological group G is a Pietsch measure for nonlinear summing mappings on closed translation invariant subspaces of C(G). This answers a question posed to the authors by J. Diestel. We also show that our result applies to several well-studied classes of nonlinear summing mappings. In the final section some problems are proposed.

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.

Regular mappings between dimensions

Guy David, Stephen Semmes (2000)

Publicacions Matemàtiques

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The notions of Lipschitz and bilipschitz mappings provide classes of mappings connected to the geometry of metric spaces in certain ways. A notion between these two is given by regular mappings (reviewed in Section 1), in which some non-bilipschitz behavior is allowed, but with limitations on this, and in a quantitative way. In this paper we look at a class of mappings called (s, t)-. These mappings are the same as ordinary regular mappings when s = t, but otherwise they behave somewhat...