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bmo ρ (ω) spaces and Riesz transforms associated to Schrödinger operators

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Abstract

We introduce the BMO-type space bmo ρ (ω) and establish the duality between h 1 ρ (ω) and bmo ρ (ω), where ω ∈ A ρ, ∞1 (ℝn) and ω’s locally behave as Muckenhoupt’s weights but actually include them. We also give the Fefferman-Stein type decomposition of bmo ρ (ω) with respect to Riesz transforms associated to Schrödinger operator ℒ, where ℒ = -Δ + V is a Schrödinger operator on ℝn (n ⩾ 3) and V is a nonnegative function satisfying the reverse Hölder inequality.

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Authors and Affiliations

  1. School of General Education, Beijing International Studies University, Beijing, 100024, China

    Hua Zhu

  2. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Qian Zhang

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  1. Hua Zhu
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  2. Qian Zhang
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Correspondence to Hua Zhu.

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Zhu, H., Zhang, Q. bmo ρ (ω) spaces and Riesz transforms associated to Schrödinger operators. Sci. China Math. 59, 1995–2018 (2016). https://doi.org/10.1007/s11425-015-0767-9

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  • DOI: https://doi.org/10.1007/s11425-015-0767-9

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