Certain Results For a Class of Nonlinear Functional Spaces

In this article, we study the properties of a class of functional spaces which arise from the investigation of nonlinear differential equations. We establish some integral inequalities then by applying these inequalities, we prove some lemmas and theorems, which indicate the relation of these spaces (pn-spaces) with the Lebesgue and Sobolev spaces in the case when pn-spaces with constant and variable exponents.