Normability of Lorentz spaces-an alternative approach

Abstrakt

We study normability properties of classical Lorentz spaces. Given certain general lattice-like structure, we first prove a general sufficient condi- tion for it's associate space to be a Banach function space.

We use this result to get an alternative proof of the Sawyer's characterization of normability of a classical Lorentz space of type Lambda. We characterize normability of a classical Lorentz space of weak type Lambda.

Klíčová slova

• weighted Lorentz space
• weighted inequality
• non-increasing rearrangement
• Banach function space
• associate space