Hardy spaces for Fourier--Bessel expansions

TL;DR

This paper investigates Hardy spaces linked to Fourier-Bessel expansions and Bessel operators, providing definitions, properties, and atomic characterizations for these function spaces on specific intervals.

Contribution

It introduces Hardy spaces for Fourier-Bessel expansions, defines them via maximal functions, and establishes atomic characterizations, advancing the understanding of these function spaces.

Findings

Defined Hardy spaces for Fourier-Bessel expansions.

Established atomic characterizations of these Hardy spaces.

Connected Hardy spaces with maximal functions of Poisson semigroups.

Abstract

We study Hardy spaces for Fourier--Bessel expansions associated with Bessel operators on $((0,1), x^{2\nu+1}\, dx)$ and $((0,1), dx)$. We define Hardy spaces $H^1$ as the sets of $L^1$-functions for which their maximal functions for the corresponding Poisson semigroups belong to $L^1$. Atomic characterizations are obtained.