Linear dilatation and differentiability of homeomorphisms of
Author:
Bruce Hanson
Journal:
Proc. Amer. Math. Soc. 140 (2012), 3541-3547
MSC (2010):
Primary 30C65; Secondary 26B05
DOI:
https://doi.org/10.1090/S0002-9939-2012-11688-0
Published electronically:
March 29, 2012
MathSciNet review:
2929022
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Abstract | References | Similar Articles | Additional Information
Abstract: According to a classical result, if is a domain in
, where
,
is a homeomorphism and the lim-sup dilatation
of
is finite almost everywhere on
, then
is differentiable almost everywhere on
. We show that this theorem fails if
is replaced by the lim-inf dilatation
. Our example demonstrates the sharpness of recent results of Kallunki and Koskela concerning the
function and also of Balogh and Csörnyei involving the lower-scaled oscillation of continuous functions
.
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Additional Information
Bruce Hanson
Affiliation:
Department of Mathematics, Statistics and Computer Science, St. Olaf College, Northfield, Minnesota 55057
Email:
hansonb@stolaf.edu
DOI:
https://doi.org/10.1090/S0002-9939-2012-11688-0
Received by editor(s):
April 12, 2011
Published electronically:
March 29, 2012
Dedicated:
In memory of Juha Heinonen
Communicated by:
Mario Bonk
Article copyright:
© Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.