Geodesic
Riemann and Hilbert boundary value problems in $BMO$ classes for holomorphic functions
Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 4, pp. 28-38

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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. 
@article{VMJ_2010_12_4_a4,
     author = {S. B. Klimentov},
     title = {Riemann and {Hilbert} boundary value problems in $BMO$ classes for holomorphic functions},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {28--38},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2010_12_4_a4/}
}
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S. B. Klimentov. Riemann and Hilbert boundary value problems in $BMO$ classes for holomorphic functions. Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 4, pp. 28-38. http://geodesic.mathdoc.fr/item/VMJ_2010_12_4_a4/