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Duality of Hardy and BMO spaces associated with operators with heat kernel bounds on product domains

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Abstract

Let L be the infinitesimal generator of an analytic semigroup on L2 (ℝ) with suitable upper bounds on its heat kernels, and L has a bounded holomorphic functional calculus on L2 (ℝ). In this article, we introduce new function spaces H 1L (ℝ × ℝ) and BMOL(ℝ × ℝ) (dual to the space H 1L* (ℝ × ℝ) in which L* is the adjoint operator of L) associated with L, and they generalize the classical Hardy and BMO spaces on product domains. We obtain a molecular decomposition of function for H 1L (ℝ × ℝ) by using the theory of tent spaces and establish a characterization of BMOL (ℝ × ℝ) in terms of Carleson conditions. We also show that the John-Nirenberg inequality holds for the space BMOL (ℝ × ℝ). Applications include large classes of differential operators such as the magnetic Schrödinger operators and second-order elliptic operators of divergence form or nondivergence form in one dimension.

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Authors and Affiliations

  1. Department of Mathematics, Zhongshan University, 510275, Guangzhou, P.R. China

    Donggao Deng, Liang Song, Chaoqiang Tan & Lixin Yan

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  1. Donggao Deng
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  2. Liang Song
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  3. Chaoqiang Tan
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  4. Lixin Yan
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Correspondence to Donggao Deng.

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Deng, D., Song, L., Tan, C. et al. Duality of Hardy and BMO spaces associated with operators with heat kernel bounds on product domains. J Geom Anal 17, 455–483 (2007). https://doi.org/10.1007/BF02922092

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  • DOI: https://doi.org/10.1007/BF02922092

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