Abstract: World Journal of Applied Mathematics and Statistics

Abstract:
In present paper, I intend to introduce our study of new normed function space type of Lorentz-Morrey ℒ (s,G) associated parameters of many groups of variables started in works by A.Dj. Djabrailov. I must note that, this space belongs to spaces type of Lebesgue-Morrey type. As an application, we give some properties for these spaces again. In addition, I have given two needing lemmas and they have been proved. In view of the embedding theorems we study some properties of the functions, which are belonging to these spaces. Although I have dealt with a lot of measurable cases, differentiable function spaces are very difficult in general. The most important cases are Lebes gue-Morrey type spaces with many groups of variables. I begin with the general theory of Mathematical Analysis, I have constructed new normed spaces type of Lorentz- Morrey, gave and proved some characterization of these type of spaces. In addition, specific techniques for introducing some embedding theorems will be given late.