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Discrete Littlewood—Paley—Stein Characterization and L2 Atomic Decomposition of Local Hardy Spaces

  • Wei DingEmail author
  • Li Xin JiangEmail author
  • Yue Ping ZhuEmail author
Article
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Abstract

Usually, the condition that T is bounded on L2(ℝn) is assumed to prove the boundedness of an operator T on a Hardy space. With this assumption, one only needs to prove the uniformly boundness of T on atoms, since T(f) = ∑iλiT (ai), provided that f = ∑iλiai in L2(ℝn), where ai is an L2 atom of this Hardy space. So far, the L2 atomic decomposition of local Hardy spaces hp(ℝn), 0 < p ≤ 1, hasn’t been established. In this paper, we will solve this problem, and also show that hp(ℝn) can also be characterized by discrete Littlewood—Paley functions.

Keywords

Local Hardy space discrete local Calderón’s identity duality atom 

MR(2010) Subject Classification

42B35 42B30 42B25 42B20 

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Notes

Acknowledgements

We thank the referees for their time and comments.

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Copyright information

© Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019

Authors and Affiliations

  1. 1.School of SciencesNantong UniversityNantongP. R. China
  2. 2.Department of MathematicsNantong Normal CollegeNantongP. R. China

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