Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 39, Tome 389 (2011), pp. 252-256
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H. Hedenmalm; N. A. Shirokov. Keldysh–Lavrentiev counterexample and means of powers of conformal mapping. 1. Construction of a mapping. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 39, Tome 389 (2011), pp. 252-256. http://geodesic.mathdoc.fr/item/ZNSL_2011_389_a13/
@article{ZNSL_2011_389_a13,
author = {H. Hedenmalm and N. A. Shirokov},
title = {Keldysh{\textendash}Lavrentiev counterexample and means of powers of conformal mapping. {1.~Construction} of a~mapping},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {252--256},
year = {2011},
volume = {389},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_389_a13/}
}
TY - JOUR
AU - H. Hedenmalm
AU - N. A. Shirokov
TI - Keldysh–Lavrentiev counterexample and means of powers of conformal mapping. 1. Construction of a mapping
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2011
SP - 252
EP - 256
VL - 389
UR - http://geodesic.mathdoc.fr/item/ZNSL_2011_389_a13/
LA - ru
ID - ZNSL_2011_389_a13
ER -
%0 Journal Article
%A H. Hedenmalm
%A N. A. Shirokov
%T Keldysh–Lavrentiev counterexample and means of powers of conformal mapping. 1. Construction of a mapping
%J Zapiski Nauchnykh Seminarov POMI
%D 2011
%P 252-256
%V 389
%U http://geodesic.mathdoc.fr/item/ZNSL_2011_389_a13/
%G ru
%F ZNSL_2011_389_a13
We construct a region with infinitely many cusps on its boundary such that it is possible to estimate the derivative of a conformal mapping of the unit disk onto this region from below. We use here some ideas taken from a construction of a famous Keldysh–Lavrentiev example.
[1] D. Kraetzer, “Experimental bound for the universal integral means spectrum of conformal maps”, Compl. Variabl. Theory Appl., 31 (1996), 305–309 | DOI | MR | Zbl
[2] I. I. Privalov, Granichnye svoistva analiticheskikh funktsii, GITTL, M.–L., 1950
