A Decomposition of the Dual Space of Some Banach Function Spaces

Claudia Capone,Maria Rosaria Formica

doi:10.1155/2012/737534

Abstract

We give a decomposition for the dual space of some Banach Function Spaces as the Zygmund space of the exponential integrable functions, the Marcinkiewicz space , and the Grand Lebesgue Space .

Highlights

Let Ω be a set of Lebesgue measure |Ω| < ∞
We give a decomposition for the dual space of some Banach Function Spaces as the Zygmund space EXPα of the exponential integrable functions, the Marcinkiewicz space Lp,∞, and the Grand Lebesgue Space Lp,θ
What is the difference between the dual space X∗ and the associate space X of a Banach Function Space X? By associate space X of X we mean the space determined by the associate norm ρ : ρ g sup fg dx : f ∈ M, ρ f ≤ 1

Summary

A Decomposition of the Dual Space of Some Banach Function Spaces

We give a decomposition for the dual space of some Banach Function Spaces as the Zygmund space EXPα of the exponential integrable functions, the Marcinkiewicz space Lp,∞, and the Grand Lebesgue Space Lp ,θ

Introduction

Preliminaries

Main Results