Riemann-Hilbert boundary value problems in BMO classes for generalized analytic functions

Klimentov S. B.
Vladikavkaz Mathematical Journal 2011. Vol. 13. Issue 1.

Abstract:
The classical Riemann--Hilbert boundary value problems for generalized analytic functions are under consideration. We search the solution in BMO class underassumption that the coefficient of the boundary condition belongs to the set of pointwise multipliers of BMO. Earlier in [2] the author constructed examples when the problem for golomorphic functions  with non-negative index in the such natural setting has no solution in BMOA. Sufficient conditions on the coefficient are given when we have usual pattern of solvability in BMO class.

Keywords: Riemann-Hilbert boundary value problems, $BMO$ classes, generalized analytic functions.

Language: Russian Download the full text