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Vladikavkaz. Mat. Zh., 2011, Volume 13, Number 1, Pages 13–20 (Mi vmj371)  

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

S. B. Klimentovab

a Southern Federal University, RUSSIA, Rostov-on-Don
b South Mathematical Institute of VSC RAS, RUSSIA, Vladikavkaz

Abstract: 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.

Key words: Riemann–Hilbert boundary value problems, $BMO$ classes, generalized analytic functions.

Full text: PDF file (158 kB)
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UDC: 517.2
Received: 02.10.2009

Citation: S. B. Klimentov, “Riemann–Hilbert boundary value problems in $BMO$ classes for generalized analytic functions”, Vladikavkaz. Mat. Zh., 13:1 (2011), 13–20

Citation in format AMSBIB
\Bibitem{Kli11}
\by S.~B.~Klimentov
\paper Riemann--Hilbert boundary value problems in $BMO$ classes for generalized analytic functions
\jour Vladikavkaz. Mat. Zh.
\yr 2011
\vol 13
\issue 1
\pages 13--20
\mathnet{http://mi.mathnet.ru/vmj371}


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