BASIS PROPERTIES OF THE SYSTEM OF EXPONENTIALS IN WEIGHTED MORREY SPACES

Abstract

In this paper the basis properties (completeness, minimality and basicity) of the system of exponentials are investigated in weighted Morrey spaces, where the weight function is defined as a product of power functions. Although the same properties of the system of exponentials, as well as their pertubations, are well studied in weighted Lebesgue spaces, the situation changes cardinally in Morrey spaces, since Morrey spaces are not separable. Nevetheless, there are works, that study these problems. In [1-3] there were studied the basis properties of the system of exponentials in Morrey space. Some approximation problems have been investigated in Morrey-Smirnov classes in [4].