H. Hedenmalm, N. A. Shirokov, “Keldysh–Lavrentiev counterexample and means of powers of conformal mapping. 1. Construction of a mapping”, Zap. Nauchn. Sem. POMI, 2011, Volume 389,Pages <nobr>252

Keldysh–Lavrentiev counterexample and means of powers of conformal mapping. 1. Construction of a mapping

H. Hedenmalm^a, N. A. Shirokov^b

^a Department of Mathematics, The Royal Institute of Technology, Stockholm, Sweden
^b Saint-Petersburg State University, Saint-Petersburg, Russia

Abstract: 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.

Key words and phrases: conformal mapping, Keldysh–Lavrentiev example.

UDC: 517.547

Received: 01.06.2011