The molecular characterization of weighted Hardy spaces

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We first define molecules for weighted Hardy spaces and prove their molecular characters. As an application, we give sufficient conditions on the kernel k such that the convolution operator T f = k * f is bounded on weighted Hardy spaces Hwp(ℝn), w ∈ A1. We also get the Hwp(ℝ), 1/2 <p ≤ 1, boundedness of the Hilbert transform and the Hwp(ℝn), n/(n+1) < p ≤ 1, boundedness of the Riesz transforms.

Original languageEnglish
Pages (from-to)442-460
Number of pages19
JournalJournal of Functional Analysis
Issue number2
StatePublished - 1 Feb 2002


  • Atomic decomposition
  • Hilbert transform
  • Molecular character
  • Riesz transforms
  • Singular integrals
  • Weighted Hardy spaces


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