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A note on weak factorization of a Meyer-type Hardy space via a Cauchy integral operator

Volume 253 / 2020

Yongsheng Han, Ji Li, Cristina Pereyra, Brett D. Wick Studia Mathematica 253 (2020), 307-327 MSC: Primary 42B35; Secondary 42B25. DOI: 10.4064/sm190209-12-8 Published online: 6 March 2020

Abstract

This paper provides a weak factorization for the Meyer-type Hardy space $H^1_b(\mathbb {R})$, and characterizations of its dual ${\rm BMO}_b(\mathbb {R})$ and its predual ${\rm VMO}_b(\mathbb {R})$ via boundedness and compactness of a suitable commutator with the Cauchy integral $\mathscr {C}_{\Gamma }$, respectively. Here $b(x)=1+iA’(x)$ where $A’\in L^{\infty }(\mathbb {R})$, and the Cauchy integral $\mathscr {C}_{\Gamma }$ is associated to the Lipschitz curve $\Gamma =\{x+iA(x): x\in \mathbb {R}\}$.

Authors

  • Yongsheng HanDepartment of Mathematics
    Auburn University
    Auburn, AL 36849, U.S.A.
    e-mail
  • Ji LiDepartment of Mathematics
    Macquarie University
    Sydney, Australia
    e-mail
  • Cristina PereyraDepartment of Mathematics and Statistics
    University of New Mexico
    Albuquerque, NM 87106, U.S.A.
    e-mail
  • Brett D. WickDepartment of Mathematics and Statistics
    Washington University in St. Louis
    St. Louis, MO 63130-4899, U.S.A.
    e-mail

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