A Moser type inequality for Bessel Laplace equations and applications

TL;DR

This paper establishes a Moser type inequality for harmonic functions related to Bessel operators and applies it to characterize Hardy spaces using maximal functions, filling a gap in the harmonic analysis of Bessel Laplace equations.

Contribution

It introduces a Moser type inequality for Bessel harmonic functions and uses it to prove equivalence of Hardy space characterizations, a novel result in this setting.

Findings

Proved a Moser type inequality for Bessel harmonic functions.

Established the equivalence of Hardy space characterizations via maximal functions.

Abstract

In this paper, we study Bessel operators and Bessel Laplace equations studied by Weinstein, Huber, and related the harmonic function theory introduced by Muckenhoupt--Stein. We establish the Moser type inequality for these harmonic functions, which is missing in this setting before. We then apply it to give a direct proof for the equivalence of characterizations of the Hardy spaces associated to Bessel operator via non-tangential maximal function and radial maximal function defined in terms of the Poisson semigroup.