MARCINKIEWICZ-TYPE INTERPOLATION THEOREM FOR LOCAL MORREY SPACES - Chigambayeva, Д. (Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences, 2024)
This paper is devoted to the proof of the interpolation theorem for local Morrey spaces. The purpose of this work is to study the interpolation properties of local Morrey spaces. The characteristic features of these spaces are analyzed. Based on the research carried out, the author proved the Marcinkiewicz-type interpolation theorem for local Morrey spaces on the homogeneous groups. This result is important both for function theory and functional analysis, and for applications. The interpolation ability of local Morrey spaces in the case of linear operators is revealed and justified. To obtain the result, interpolation methods for function spaces, embedding properties, and methods of functional analysis were used. The real Peetre method was used as an interpolation method and Hӧlder's, Minkowski's, Hardy's inequalities as the basic inequalities of function analysis were used. On the basis of the research, it should be noted that in the case of linear operators the scale of these spaces is interpolational in contrast to the classical Morrey spaces.