Hardy spaces and Campanato spaces associated with Laguerre expansions and higher order Riesz transforms

2025/04/14 by The Anh Bui, Bui, The Anh, Xuan Thinh Duong +1
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2504.09867

openalex publication_date 2025/04/14 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

Let \(L_ν\) be the Laguerre differential operator which is the self-adjoint extension of the differential operator L_ν:= ∑_i=1ⁿ [-(∂²)/(∂ x_i²) + x_i² + (1)/(x_i²) (ν_i² - (1)/(4) ) ] initially defined on \(C_c^∞(ℝ₊ⁿ)\) as its natural domain, where \(ν∈ [-1/2,∞)ⁿ\), \(n ≥ 1\). In this paper, we first develop the theory of Hardy spaces \(H^p_Lν\) associated with \(L_ν\) for the full range \(p ∈ (0,1]\). Then we investigate the corresponding BMO-type spaces and establish that they coincide with the dual spaces of \(H^p_Lν\). Finally, we show boundedness of higher-order Riesz transforms on Lebesgue spaces, as well as on our new Hardy and BMO-type spaces.

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