Predual of weak Orlicz spaces
Naoya Hatano, Ryota Kawasumi, and Takahiro Ono
TL;DR
This paper studies the predual spaces of weak Orlicz spaces, introduces Orlicz-Lorentz spaces, and establishes boundedness of the Hardy-Littlewood maximal operator, leading to a Fefferman-Stein inequality.
Contribution
It introduces Orlicz-Lorentz spaces and proves the boundedness of the Hardy-Littlewood maximal operator on them, enabling new inequalities for weak Orlicz spaces.
Findings
Established the boundedness of the Hardy-Littlewood maximal operator on Orlicz-Lorentz spaces
Proved the Fefferman-Stein vector-valued maximal inequality for weak Orlicz spaces
Characterized the predual spaces of weak Orlicz spaces
Abstract
In this paper, we consider the predual spaces of weak Orlicz spaces. As an application, we provide the Fefferman-Stein vector-valued maximal inequality for the weak Orlicz spaces. In order to prove this statement, we introduced the Orlicz-Lorentz spaces, and showed the boundedness of the Hardy-Littlewood maximal operator on these spaces.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Holomorphic and Operator Theory · Advanced Banach Space Theory