Weighted local Hardy spaces associated to Schrödinger operators

2014/03/29 by Hua Zhu, Lin Tang, Zhu, Hua +1
Mathematics · #42B20 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #Primary 42B30 #Secondary 42B25

paper · pdf · doi:10.48550/arxiv.1403.7641

openalex publication_date 2014/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we characterize the weighted local Hardy spaces h^p_ρ(ω) related to the critical radius function ρ and weights ω∈ A_∞^{ρ, ∞}(ℝⁿ) which locally behave as Muckenhoupt's weights and actually include them, by the local vertical maximal function, the local nontangential maximal function and the atomic decomposition. By the atomic characterization, we also prove the existence of finite atomic decompositions associated with h^p_ρ(ω). Furthermore, we establish boundedness in h^p_ρ(ω) of quasi- Banach-valued sublinear operators. As their applications, we establish the equivalence of the weighted local Hardy space h¹_ρ(ω) and the weighted Hardy space H¹_{\cal L}(ω) associated to Schrödinger operators \cal L with ω∈ A₁^ρ,∞(ℝⁿ)

Citations

• Weighted norm inequalities for Schrödinger type operators
• Hp spaces of several variables
• Extrapolation from A_\fz^ρ,\fz, vector-valued inequalities and applications in the Schrödinger settings

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• The Atomic Characterization of Weighted Local Hardy Spaces and Its Applications
• Riesz transforms associated with Schrödinger operators acting on weighted Hardy spaces
• New Atomic Decompositions of Weighted Local Hardy Spaces
• Weighted local Hardy spaces and their applications