ON THE SOLVABILITY OF THE HOMOGENEOUS RIEMANN PROBLEM IN THE MORREY-HARDY CLASSES

Abstract

The homogeneous Riemann boundary value problem for analytic functions in Morrey-Hardy classes is considered. In this case, some properties of functions from these classes are studied and the possibility of representing these functions in terms of an integral of Cauchy type is established. The specificity of these problems lies in the fact that the Morrey space  L ^p,α   is not separable. Therefore, we consider a subspace  M ^p,α  ⊂  L ^p,α in which the continuous functions are dense. From the point of view of the approximation theory, the space  M ^p,α   is of special interest. The corresponding Morrey-Hardy classes generated by the space  M  ^p,α  are defined and the solvability problems of Riemann problems in these classes are studied.