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 | Abstract: | 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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