Real-variable Characterizations of Orlicz-Hardy Spaces on Strongly Lipschitz Domains of ℝⁿ

2011/07/17 by Dachun Yang, Yang, Dachun, Sibei Yang +1
Mathematics · #35J25 #42B20 #42B25 #42B37 #47B38 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations #Primary: 42B30 #Secondary: 42B35 #math.CA #math.FA #msc:35J25 #msc:42B20 #msc:42B25 #msc:42B30 #msc:42B35 #msc:42B37 #msc:47B38

paper · pdf · doi:10.48550/arxiv.1107.3267

65 pages, Rev. Mat. Iberoam. (to appear)

arxiv created 2011/07/17 · openalex publication_date 2011/07/17 · arxiv updated 2011/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Ω be a strongly Lipschitz domain of ℝⁿ, whose complement in ℝⁿ is unbounded. Let L be a second order divergence form elliptic operator on L² (Ω) with the Dirichlet boundary condition, and the heat semigroup generated by L have the Gaussian property (G_diam(Ω)) with the regularity of their kernels measured by μ∈(0,1], where diam(Ω) denotes the diameter of Ω. Let Φ be a continuous, strictly increasing, subadditive and positive function on (0,∞) of upper type 1 and of strictly critical lower type p_Φ∈(n/(n+μ),1]. In this paper, the authors introduce the Orlicz-Hardy space H_{Φ, r}(Ω) by restricting arbitrary elements of the Orlicz-Hardy space H_Φ(ℝⁿ) to \boz and establish its atomic decomposition by means of the Lusin area function associated with \e^-tL\_t≥0. Applying this, the authors obtain two equivalent characterizations of H_{Φ, r}(\boz) in terms of the nontangential maximal function and the Lusin area function associated with the heat semigroup generated by L.

Citations

• Generalizations of Lipschitz spaces and an application to Hardy spaces and bounded mean oscillation
• Some new function spaces and their applications to Harmonic analysis
• Hp spaces of several variables
• Some Maximal Inequalities

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