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

The classical Riemann–Hilbert boundary value problems for generalized analytic functions are under consideration. We search the solution in $BMO$ class under assumption 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.