Aggrandization of spaces: a new general approach and application

Abstract

Our study is based on recent results concerning the so-called local aggrandization of Lebesgue spaces. We extend this framework to the case of arbitrary Banach spaces of functions on metric spaces. Furthermore, we demonstrate that grand spaces of holomorphic functions can be equivalently defined through aggrandization associated exclusively with the boundary. This paper review presents recent results obtained in collaboration with Stefan Samko and provides a concise introduction to the classical theory of grand spaces for comparative analysis. We also discuss the underlying motivation for investigating these spaces.