Discrete variant of Morrey spaces. New approach

It is well known that for study of specific analysis operators, for example, the Hilbert operator, the Hardy-Littlewood maximal function operator, etc., it is very important to choose the right spaces in which we can describe the various properties of these operators.
Recently, the spaces $M_{\lambda, L^p}$ introduced by Morrey, and their generalizations that arise in the study of partial differential equations have begun to play an important role in analysis.
In this report, I'll talk about a new series of spaces containing Morrey spaces. Based on a new approach for this series of spaces, a number of duality, interpolation and extrapolation theorems are proved, and a description of the multiplicator space is obtained. We note that the application of the obtained results to the classical Morrey spaces made it possible to solve several important problems there as well.