A Moser type inequality for Bessel Laplace equations and applications

2016/07/14 by Xuan Thinh Duong, Duong, Xuan Thinh, Zihua Guo +5
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1607.04101

openalex publication_date 2016/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Hp spaces of several variables
• Characterizations of product Hardy spaces in Bessel setting

Related

• Characterizations of product Hardy spaces in Bessel setting
• Hardy spaces for Fourier--Bessel expansions
• Extension of Huygens type inequalities for Bessel and modified Bessel Functions
• Generalized Huygens types inequalities for Bessel and modified Bessel functions
• Lipschitz type spaces and Landau-Bloch type theorems for harmonic functions and Poisson equations