Real-Variable Characterizations Of Hardy Spaces Associated With Bessel Operators

TL;DR

This paper characterizes Hardy spaces associated with Bessel operators using various maximal and square function approaches, providing new insights into their structure and Riesz transform relations.

Contribution

It introduces novel characterizations of Hardy spaces linked to Bessel operators via multiple analytical tools, expanding understanding of these function spaces.

Findings

Characterizations via radial, nontangential, and grand maximal functions

Establishment of Littlewood-Paley g-function and Lusin-area function descriptions

Riesz transform characterization of Hardy spaces

Abstract

Let $\lambda>0$, $p\in((2\lz+1)/(2\lz+2), 1]$, and $\triangle_\lambda\equiv-\frac{d^2}{dx^2}-\frac{2\lambda}{x} \frac d{dx}$ be the Bessel operator. In this paper, the authors establish the characterizations of atomic Hardy spaces $H^p((0, \infty), dm_\lambda)$ associated with $\triangle_\lambda$ in terms of the radial maximal function, the nontangential maximal function, the grand maximal function, the Littlewood-Paley $g$-function and the Lusin-area function, where $dm_\lambda(x)\equiv x^{2\lambda}\,dx$. As an application, the authors further obtain the Riesz transform characterization of these Hardy spaces.