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 

Show full item record


checked on May 30, 2023

Page view(s)

checked on May 31, 2023

Google ScholarTM




Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.