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Duality theory of weighted Hardy spaces with arbitrary number of parameters

  • Guozhen Lu EMAIL logo und Zhuoping Ruan
Veröffentlicht/Copyright: 1. Mai 2012
Forum Mathematicum
Aus der Zeitschrift Forum Mathematicum Band 26 Heft 5

Abstract

In this paper, we use the discrete Littlewood–Paley–Stein analysis to get the duality result of the weighted product Hardy space for arbitrary number of parameters under a rather weak condition on the product weight w∈A∞(ℝn1×⋯×ℝnk). We will show that for any k ≥ 2, (Hwp(ℝn1×⋯×ℝnk))*=CMOwp(ℝn1×⋯×ℝnk) (a generalized Carleson measure), and obtain the boundedness of singular integral operators on BMO w. Our theorems even when the weight function w = 1 extend the H1-BMO duality of Chang–R. Fefferman for the non-weighted two-parameter Hardy space H1(ℝn×ℝm) to Hp(ℝn1×⋯×ℝnk) for all 0<p≤1 and our weighted theory extends the duality result of Krug–Torchinsky on weighted Hardy spaces Hwp(ℝn×ℝm) for w∈Ar(ℝn×ℝm) with 1≤r≤2 and r/2<p≤1 to Hwp(ℝn1×⋯×ℝnk) with w∈A∞(ℝn1×⋯×ℝnk) for all 0<p≤1.

Keywords: Duality; weighted Hardy space; discrete Littlewood-Paley-Stein analysis; Caderón's identity; Max–Min type inequality; multiparameter A∞ weight; multiparameter singular integrals
MSC: 42B20; 42B30; 42B35

Funding source: US NSF

Award Identifier / Grant number: DMS0901761

Funding source: NSFC

Award Identifier / Grant number: 1117145

Received: 2012-2-25
Published Online: 2012-5-1
Published in Print: 2014-9-1

© 2015 by De Gruyter

Artikel in diesem Heft

  1. Frontmatter
  2. Weighted norm inequalities for multilinear Calderón–Zygmund operators on non-homogeneous metric measure spaces
  3. A characterization of degree two Siegel cusp forms by the growth of their Fourier coefficients
  4. Weyl groups for non-classical restricted Lie algebras and the Chevalley Restriction Theorem
  5. An Lp-theory for non-divergence form SPDEs driven by Lévy processes
  6. Clifford–Wolf translations of Finsler spaces
  7. Duality theory of weighted Hardy spaces with arbitrary number of parameters
  8. Group algebras whose symmetric elements are Lie metabelian
  9. Algebraic supergroups of Cartan type
  10. On the K- and L-theory of hyperbolic and virtually finitely generated abelian groups
https://doi.org/10.1515/forum-2012-0018
Schlagwörter für diesen Artikel
Duality; weighted Hardy space; discrete Littlewood-Paley-Stein analysis; Caderón's identity; Max–Min type inequality; multiparameter A∞ weight; multiparameter singular integrals

Artikel in diesem Heft

  1. Frontmatter
  2. Weighted norm inequalities for multilinear Calderón–Zygmund operators on non-homogeneous metric measure spaces
  3. A characterization of degree two Siegel cusp forms by the growth of their Fourier coefficients
  4. Weyl groups for non-classical restricted Lie algebras and the Chevalley Restriction Theorem
  5. An Lp-theory for non-divergence form SPDEs driven by Lévy processes
  6. Clifford–Wolf translations of Finsler spaces
  7. Duality theory of weighted Hardy spaces with arbitrary number of parameters
  8. Group algebras whose symmetric elements are Lie metabelian
  9. Algebraic supergroups of Cartan type
  10. On the K- and L-theory of hyperbolic and virtually finitely generated abelian groups
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