In this paper, we consider Banach spaces of functions of Morrey–Hardy, Morrey–Smirnov and Morrey–Lebesgue type. Basicity of exponential system and its parts in these spaces is proved.

This work considers the Riemann boundary value problem with the piecewise continuous coefficient in Morrey-Hardy classes. Under some conditions on the coefficient, the Fredholmness of this problem is studied and the general solution of homogeneous and non-homogeneous problems in Morrey-Hardy classes is constructed. The obtained results are applied to the study of basis properties of the system of exponents with a piecewise linear phase in Morrey-Lebesgue space.

This work considers the Riemann boundary value problem with the piecewise continuous coefficient in Morrey-Hardy classes. Under some conditions on the coefficient, the Fredholmness of this problem is studied and the general solution of homogeneous problems in Morrey-Hardy classes is constructed.