Discrete Littlewood-Paley-Stein theory and multi-parameter Hardy spaces associated with flag singular integrals

By Yongsheng Han, G. Lu. 2008

55 citations recorded by the source corpus.

The main purpose of this paper is to develop a unified approach of multi-parameter Hardy space theory using the discrete Littlewood-Paley-Stein analysis in the setting of implicit multi-parameter structure. It is motivated by the goal to establish and develop the Hardy space theory for the flag singular integral operators studied by Muller-Ricci-Stein and Nagel-Ricci-Stein. This approach enables us to avoid the use of transference method of Coifman-Weiss as often used in the $L^p$ theory for $p>1$ and establish the Hardy spaces $H^p_F$ and its dual spaces associated with the flag singular integral operators for all $0<p\leq 1$. We also prove the boundedness of flag singular integral operators on $BMO_F$ and $H^p_F$, and from $H^p_F$ to $L^p$ for all $0<p\le 1$ without using the deep atomic decomposition. As a result, it bypasses the use of Journe's type covering lemma in this implicit multi-parameter structure. The method used here provides alternate approaches of those developed by Chang, R. Fefferman, Journe and Pipher in the pure product setting. A Calderon-Zygmund decomposition and interpolation theorem are also proved for the implicit multi-parameter Hardy spaces.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0892e47017942320e11c192506cb523a672efb97

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In Applied Mathematics

  1. Eric T. Sawyer
  2. Yongsheng Han
  3. G. Lu
  4. Nguyen Huong Lam
  5. Dachun Yang
  6. Tuomas Hytönen
  7. Caifeng Zhang
  8. Y. Yang

In Mathematical Physics

  1. Eric T. Sawyer
  2. G. Lu
  3. Yongsheng Han
  4. Dachun Yang
  5. Nguyen Huong Lam
  6. Tuomas Hytönen
  7. Y. Yang
  8. Ji Li

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