### A new class of function spaces on domains of $\mathbb{R}^d$ and its relations to classical function spaces

Document Type : Research Paper

Author

Department of Mathematics and Applications, Faculty of Basic Sciences, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran

Abstract

A new class of function spaces on domains (i.e., open and connected subsets) of $\mathbb{R}^d$, by means of the asymptotic behavior of modulations of functions and distributions, is defined. This class contains the classes of Lebesgue spaces and modulation spaces. Main properties of this class are studied, its applications in the study of function spaces and its relations to classical function spaces are discussed.

Keywords