Characterizations of Lorentz Type Sobolev Multiplier Spaces and Their Preduals

TL;DR

This paper characterizes Lorentz type Sobolev multiplier spaces and their preduals, explores their dual structures, and demonstrates the boundedness of the local Hardy-Littlewood maximal function on these spaces.

Contribution

It introduces new characterizations of Lorentz Sobolev multiplier spaces and analyzes their preduals, including block decompositions and duality properties.

Findings

Characterizations of Lorentz Sobolev multiplier spaces

Analysis of their preduals and K"othe duals

Boundedness of the local Hardy-Littlewood maximal function

Abstract

We provide several characterizations of Sobolev multiplier spaces of Lorentz type and their preduals. Block decomposition and K\"othe dual of such preduals are discussed. As an application, the boundedness of local Hardy-Littlewood maximal function on these spaces will be justified.