Hardy spaces, Campanato spaces and higher order Riesz transforms associated with Bessel operators

2025/04/16 by The Anh Bui, Bui, The Anh
Mathematics · #Advanced Harmonic Analysis Research #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2504.11758

Abstract

Let ν= (ν₁, …, ν_n) ∈ (-1/2, ∞)ⁿ, with n ≥ 1, and let Δ_ν be the multivariate Bessel operator defined by Δ_ν = -∑_j=1ⁿ( (∂²)/(∂ x_j²) - (ν_j² - 1/4)/(x_j²) ). In this paper, we develop the theory of Hardy spaces and BMO-type spaces associated with the Bessel operator Δ_ν. We then study the higher-order Riesz transforms associated with Δ_ν. First, we show that these transforms are Calderón-Zygmund operators. We further prove that they are bounded on the Hardy spaces and BMO-type spaces associated with Δ_ν.

Related

• Hardy spaces and Campanato spaces associated with Laguerre expansions and higher order Riesz transforms
• Riesz transforms, Hardy spaces and Campanato spaces associated with Laguerre expansions
• Characterizations of product Hardy spaces in Bessel setting
• Product Hardy, BMO spaces and iterated commutators associated with Bessel Schrödinger operators
• Real-Variable Characterizations Of Hardy Spaces Associated With Bessel Operators