JournalsrmiVol. 29, No. 4pp. 1127–1157

Hardy spaces associated with different homogeneities and boundedness of composition operators

  • Yongsheng Han

    Auburn University, USA
  • Chincheng Lin

    National Central University, Chung-Li, Taiwan
  • Guozhen Lu

    Wayne State University, Detroit, USA
  • Zhuoping Ruan

    Nanjing University, China
  • Eric T. Sawyer

    McMaster University, Hamilton, Canada
Hardy spaces associated with different homogeneities and boundedness of  composition operators cover
Download PDF

Abstract

It is well known that standard Calderón–Zygmund singular integral operators with isotropic and nonisotropic homogeneities are bounded on the classical Hp(Rm)H^p(\mathbb{R}^m) and nonisotropic Hhp(Rm),H^p_{h}(\mathbb{R}^m), respectively. In this paper, we develop a new Hardy space theory and prove that the composition of two Calderón–Zygmund singular integral operators with different homogeneities is bounded on this new Hardy space. Such a Hardy space has a multiparameter structure associated with the underlying mixed homogeneities arising from the two singular integral operators under consideration. The Calderón–Zygmund decomposition and an interpolation theorem hold on these new Hardy spaces.

Cite this article

Yongsheng Han, Chincheng Lin, Guozhen Lu, Zhuoping Ruan, Eric T. Sawyer, Hardy spaces associated with different homogeneities and boundedness of composition operators. Rev. Mat. Iberoam. 29 (2013), no. 4, pp. 1127–1157

DOI 10.4171/RMI/751