Interpolation theorem for Marcinkiewicz spaces with applications to Lorentz gamma spaces

Abstract

This paper is devoted to the interpolation principle between spaces of weak type. We characterise interpolation spaces between two Marcinkiewicz spaces in terms of Hardy type operators involving suprema.

We study general properties of such operators and their behavior on Lorentz gamma spaces. Aparticular emphasis is placed on elementary and comprehensive proofs.

Keywords

• interpolation
• Lorentz gamma space
• Marcinkiewicz space
• supremum operator