Some Characterization of the Function Space Type of Lizorkin−Triebel−Morrey

Abstract

This paper will introduce you to some properties of normed function spaces with many groups variables field of Analysis and it helps me appreciate how normed Lebesgue–Morrey space with many groups of variables that build and studied new normed spaces nowadays. Many of the topics here are important to an Analysis class. By reading this paper, you will discover the “embedding theory” of normed spaces type of Lebesgue–Morrey by introducing few of its “new functions with groups with variables” and along the way you will see to some interesting and article elements of the branch called Analysis. A lot of problems belonging to the characterization of various spaces of differentiability function spaces and relationships between them have been solved using the theory embedding theorems. The purpose of this paper is to review several embedding inequalities of normed spaces that will arise properties of these spaces and again throughout this material. We also give “working definition, notations” of a functions and function spaces. We must note that, the analysis is based on such function spaces to build new space type of Lizorkin–Triebel–Morrey. In addition, throughout this paper we will introduce a working normed function spaces type of Lizorkin–Triebel–Morrey with standard mathematical definitions and terminology. One aspect of this paper involves normed Lebesgue–Morey type spaces that can convert space from one to another.