Riesz transforms, Hardy spaces and Campanato spaces associated with Laguerre expansions

2024/11/28 by The Anh Bui, Bui, The Anh
Mathematics · #42B30 #42B35 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2411.19403

openalex publication_date 2024/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let ν∈ [-1/2,∞)ⁿ, n≥ 1, and let L_ν be a self-adjoint extension of the differential operator L_ν:= ∑_i=1ⁿ [-(∂²)/(∂ x_i²) + x_i² + (1)/(x_i²)(ν_i² - (1)/(4))] on C_c^∞(ℝ₊ⁿ) as the natural domain. In this paper, we first prove that the Riesz transform associated with \mathcal L_ν is a Calderón-Zygmund operator, answering the open problem in [JFA, 244 (2007), 399-443]. In addition, we develop the theory of Hardy spaces and Campanato spaces associated with L_ν. As applications, we prove that the Riesz transform related to L_ν is bounded on these Hardy spaces and Campanato spaces, completing the description of the boundedness of the Riesz transform in the Laguerre expansion setting.

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