Authors: Arsenović, Miloš
Todorčević, Vesna 
Näkki, Raimo
Title: Boundary modulus of continuity and quasiconformal mappings
Journal: Annales Academiae Scientiarum Fennicae Mathematica
Volume: 37
Issue: 1
First page: 107
Last page: 118
Issue Date: 1-Feb-2012
Rank: M21
ISSN: 1239-629X
DOI: 10.5186/aasfm.2012.3718
Let D be a bounded domain in R n, n ≥ 2, and let f be a continuous mapping of D into R n which is quasiconformal in D. Suppose that |f(x) - f(y)| ≤ ω(|x - y|) for all x and y in ∂D, where ω is a non-negative non-decreasing function satisfying ω(2t) ≤ 2ω(t) for t ≥ 0. We prove, with an additional growth condition on ω, that |f(x) - f(y)| ≤ C maxf{ω(|x - y|); |x - y| α} for all x; y ∈ D, where α = K I(f) 1/(1-n).
Keywords: Modulus of continuity | Quasiconformal mapping
Publisher: Academia Scientiarum Fennica
Project: Function spaces and their operators 

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