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On the weak L p-Hodge decomposition and Beurling–Ahlfors transforms on complete Riemannian manifolds
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  • Published: 02 March 2010

On the weak L p-Hodge decomposition and Beurling–Ahlfors transforms on complete Riemannian manifolds

  • Xiang-Dong Li1,2,3 

Probability Theory and Related Fields volume 150, pages 111–144 (2011)Cite this article

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  • 9 Citations

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An Erratum to this article was published on 19 April 2014

Abstract

Based on a new martingale representation formula, we prove some quantitative upper bound estimates of the L p-norm of some singular integral operators on complete Riemannian manifolds. This leads us to establish the Weak L p-Hodge decomposition theorem and to prove the L p-boundedness of the Beurling–Ahlfors transforms on complete non-compact Riemannian manifolds with non-negative Weitzenböck curvature operator.

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Author information

Authors and Affiliations

  1. Institute of Applied Mathematics, AMSS, CAS, No. 55, Zhongguancun East Road, Beijing, 100190, People’s Republic of China

    Xiang-Dong Li

  2. School of Mathematical Sciences, Fudan University, 220, Handan Road, Shanghai, 200433, People’s Republic of China

    Xiang-Dong Li

  3. Institut de Mathématiques, Université Paul Sabatier, 118, route de Narbonne, 31062, Toulouse Cedex 9, France

    Xiang-Dong Li

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  1. Xiang-Dong Li
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Corresponding author

Correspondence to Xiang-Dong Li.

Additional information

X.-D. Li research was partially supported by Hundred Talents Project of the Chinese Academy of Sciences, NSFC No. 10971032, Shanghai Pujiang Talent Project No. 09PJ1401600 and Key Laboratory RCSDS, CAS, No. 2008DP173182.

An erratum to this article is available at http://dx.doi.org/10.1007/s00440-014-0561-0.

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Cite this article

Li, XD. On the weak L p-Hodge decomposition and Beurling–Ahlfors transforms on complete Riemannian manifolds. Probab. Theory Relat. Fields 150, 111–144 (2011). https://doi.org/10.1007/s00440-010-0270-2

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  • Received: 08 December 2008

  • Revised: 02 February 2010

  • Published: 02 March 2010

  • Issue Date: June 2011

  • DOI: https://doi.org/10.1007/s00440-010-0270-2

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Keywords

  • Beurling–Ahlfors transforms
  • Hodge decomposition
  • Martingale representation formula
  • Weitzenböck curvature

Mathematics Subject Classification (2000)

  • Primary 58A14
  • 58J35
  • Secondary 58J40
  • 58J65
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