S. B. Klimentov, “Representations of the “second kind” for the hardy classes of solutions to the Beltrami equation”, Sibirsk. Mat. Zh., 2014, Volume 55, Number 2,Pages <nobr>324

This article is cited in 6 papers

Representations of the “second kind” for the hardy classes of solutions to the Beltrami equation

S. B. Klimentov^ab

^a Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia
^b Southern Federal University, Rostov-on-Don, Russia

Abstract: We give examples of the absence of representations of the “second kind” for a Beltrami equation. Some sufficient conditions are proposed for the existence of these representations. We specify the regularity “up to the boundary” of a quasiconformal homeomorphism of the unit circle onto itself in the case of a regular complex characteristic.

Keywords: Beltrami equation, Hardy class, representation of the second kind.

UDC: 517.518.234+517.548.3

Received: 29.06.2013