On the solvability of the Riemann boundary value problem in Morrey--Hardy classes

Abstract

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 nonhomogeneous problems in Morrey-Hardy classes is constructed.

On Basicity of the System of Exponents with Linear Phase in Morrey-Lebesgue Space

“…When studying non-homogeneous Riemann boundary value problem, we will essentially use the following lemma from [46].…”

“…From Lemma 2.1 follows that the function A −1 ( • ) f ( • ) belongs to the spaceL p,α . Therefore, if the inequality (8) are fulfilled, as it follows from Theorem 10 [46] the problem (7) is uniquely solvable in class MH p,α + × −1 MH p,α − , and this solution can be represented as an integral…”

Relationship Between an Atomic Decomposition of Double and Unary Systems in Grand-Lebesgue Spaces

“…[26], Adams [27], S. Samko [28], Kokilashvili [29], R.E.Castilo, H.Rafeiro [30], H. A. Fiorenza, G. E. Karadzhov [31], B.T. Bilalov, T.B.Gasymov, A.A. Guliyeva [32] etc.). Along with this, of course, one has to study approximation matters in suchlike spaces.…”

Basis Properties of Exponential Systems With Linear Phases in Morrey-Sobolev Type Spaces

“…Also, in [24] the basis properties of the perturbed systems of exponentials in Morrey space have been investigated. On the other hand, the Riemann boundary value problem in Morrey-Hardy classes has been studied in [25].…”