On solvability of homogeneous Riemann boundary value problems in Hardy-Orlicz classes

Abstract

This work deals with the Orlicz space and the Hardy-Orlicz classes generated by this space, which consist of analytic functions inside and outside the unit disk. The homogeneous Riemann boundary value problems with piecewise continuous coefficients are considered in these classes. New characteristic of Orlicz space is defined which depends on whether the power function belongs to this space or not. Relationship between this characteristic and Boyd indices of Orlicz space is established. The concept of canonical solution of homogeneous problem is defined, which depends on the argument of the coefficient. In terms of the above characteristic, a condition on the jumps of the argument is found which is sufficient for solvability of these problems, and, in case of solvability, a general solution is constructed. It is established the basicity of the parts of exponential system in Hardy-Orlicz classes.