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Weak Factorizations of the Hardy space $H^1(\mathbb{R}^n)$ in terms of Multilinear Riesz Transforms

  Published:2017-06-21
 Printed: Sep 2017
  • Ji Li,
    Department of Mathematics, Macquarie University, NSW, 2109, Australia
  • Brett D. Wick,
    Department of Mathematics, Washington University-St. Louis, St. Louis, MO 63130-4899 USA
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Abstract

This paper provides a constructive proof of the weak factorization of the classical Hardy space $H^1(\mathbb{R}^n)$ in terms of multilinear Riesz transforms. As a direct application, we obtain a new proof of the characterization of ${\rm BMO}(\mathbb{R}^n)$ (the dual of $H^1(\mathbb{R}^n)$) via commutators of the multilinear Riesz transforms.
Keywords: Hardy space, BMO space, multilinear Riesz transform, weak factorization Hardy space, BMO space, multilinear Riesz transform, weak factorization
MSC Classifications: 42B35, 42B20 show english descriptions Function spaces arising in harmonic analysis
Singular and oscillatory integrals (Calderon-Zygmund, etc.)
42B35 - Function spaces arising in harmonic analysis
42B20 - Singular and oscillatory integrals (Calderon-Zygmund, etc.)
 

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