Cpmposed Grand Lebesgue Spaces

TL;DR

This paper introduces Composed Grand Lebesgue Spaces, a new class of rearrangement invariant Banach spaces, generalizing known spaces and analyzing their properties, including fundamental functions, indices, and operator boundedness.

Contribution

It defines and studies the properties of Composed Grand Lebesgue Spaces, extending the theory of Grand Lebesgue Spaces with new structural and functional insights.

Findings

Calculated Boyd's indices for CGLS.

Established boundedness of certain operators in CGLS.

Proved CGLS has the absolute continuous norm property.

Abstract

In this article we introduce and investigate a new class of rearrangement invariant (r.i.) Banach function spaces, so-called Composed Grand Lebesgue Spaces (CGLS), in particular, Integral Grand Lebesgue Spaces (IGLS), which are some generalizations of known Grand Lebesgue Spaces (GLS). We consider the fundamental functions of CGLS, calculate its Boyd's indices, obtain the norm boundedness some (regular and singular) operators in this spaces, investigate the conjugate and associate spaces, show that CGLS obeys the absolute continuous norm property etc.