Real-Variable Characterizations of Orlicz-Slice Hardy Spaces

TL;DR

This paper introduces Orlicz-slice Hardy spaces, generalizing existing Hardy spaces, and provides their characterizations, dual spaces, and boundedness criteria for Calderón-Zygmund operators, advancing the understanding of these function spaces.

Contribution

The paper defines Orlicz-slice Hardy spaces and establishes their characterizations, dual spaces, and operator boundedness, extending prior Hardy space theories.

Findings

Characterizations via atoms, molecules, and maximal functions

Finite atomic decompositions and dual space descriptions

Boundedness of Calderón-Zygmund operators on these spaces

Abstract

In this article, the authors first introduce a class of Orlicz-slice spaces which generalize the slice spaces recently studied by P. Auscher et al. Based on these Orlicz-slice spaces, the authors introduce a new kind of Hardy type spaces, the Orlicz-slice Hardy spaces, via the radial maximal functions. This new scale of Orlicz-slice Hardy spaces contains the variant of the Orlicz-Hardy space of A. Bonami and J. Feuto as well as the Hardy-amalgam space of Z. V. de P. Abl\'e and J. Feuto as special cases. Their characterizations via the atom, the molecule, various maximal functions, the Poisson integral and the Littlewood-Paley functions are also obtained. As an application of these characterizations, the authors establish their finite atomic characterizations, which further induce a description of their dual spaces and a criterion on the boundedness of sublinear operators from these Orlicz-slice Hardy spaces into a quasi-Banach space. Then, applying this criterion, the authors obtain the boundedness of $\delta$-type Calder\'on-Zygmund operators on these Orlicz-slice Hardy spaces. All these results are new even for slice Hardy spaces and, moreover, for Hardy-amalgam spaces, the Littlewood-Paley function characterizations, the dual spaces and the boundedness of $\delta$-type Calder\'on-Zygmund operators on these Hardy-type spaces are also new.