Some Characterization of the Function Space Type of Lebesgue−Morrey

As in many areas of Mathematics, we need precise definition and some characterization of function space in order to be absolutely clear. This paper seeks to do that and introduces new definitions and notations to aid our study. I also look at reversible processes of proofs and a new type of function spaces. In this scientific paper we have studied new sub of functions, sub of space of these functions. The new function spaces were investigated in this paper. In the present scientific work we have studied the differentiability functions, some differentiability properties of this type function and in particular, characterization of the differentiability spaces for the functions many groups of variables. At the start of this paper, you will see list of markings that are covered in the paper. Then I gave definition of new normed funksion spase. Following you can see several caharacterization of these spaces and proofs of these caracterization too. Finally, there is connection, known as the Fundamental Analysis, between functions and derivatives of these functions which makes the characterization of functions spaces as a practical tool for science and engineering. The function space is also use to solve many interesting problems some scientific branches like economics, finance, informatics and probability.