The Geometry of the Functional Space Type of Lebesgue-Morrey with Many Groups of Variables

In mathematics as in everyday life we encounter the concept of the mathematics. We can speak of the space of function with many groups of variables on the plane of Analysis, Function Analysis and so on. The concept of a space is not so general that it would be difficult to give it a definition which would not reduce to simply replacing the word “norm” by one of the equivalent expressions: Lebesgue-Morrey, Bessov-Morrey, etc. The concept of normed function spaces plays an extraordinarily important role in modern mathematics not only because the theory of space itself has become at the present time a very extensive and comprehensive discipline but mainly because of the influence which the theory of spaces, arising at the end of the last century, exerted and still exerts on mathematics as a whole. Here we shall briefly discuss only those very basic normed spaces concepts which will be used in the following areas. The geometry of functional Analysis and functional spaces aims at presenting the theorems and methods of modern mathematics and giving several applications in Geometry and Function Analysis. It is in fact an important theory for mathematics, since introducing some new relationship between Function analysis and Geometry. In this article I discuss some new results which stand between geometry, analysis and functional analysis.