This article is cited in 2 papers

Riemann and Hilbert boundary value problems in $BMO$ classes for holomorphic functions

S. B. Klimentov<sup>ab

a</sup> Southern Federal University, Russia, Rostov-on-Don
^b South Mathematical Institute of VSC RAS, Russia, Vladikavkaz

Abstract: The classical Riemann and Hilbert boundary value problems for analytic functions are under consideration. We search the solution in $BMOA$ class under assumption that the coefficient of the boundary condition belongs to the set of pointwise multipliers of $BMO$. We constract examples when the problem with non-negative index in the such natural setting has not solution in $BMOA$. Sufficient conditions on the coefficient are given when we have usual pattern of solvability in $BMOA$ class.

Key words: Riemann and Hilbert boundary value problems, $BMO$ classes.

UDC: 517.11

Received: 21.09.2009