Science in China Series A: Mathematics

, Volume 42, Issue 12, pp 1233–1245

A class of singular integrals on then-complex unit sphere

  • Michael Cowling
  • Tao Qian
Article

DOI: 10.1007/BF02876023

Cite this article as:
Cowling, M. & Qian, T. Sci. China Ser. A-Math. (1999) 42: 1233. doi:10.1007/BF02876023

Abstract

The operaton on the n-complex unit sphere under study have three forms: the singular integrals with holomorphic kernels, the bounded and holomorphic Fourier multipliers, and the Cauchy-Dunford bounded and holomorphic functional calculus of the radial Dirac operator\(D = \sum\nolimits_{k = 1}^n {z_k \frac{\partial }{{\partial _{z_k } }}} \). The equivalence between the three fom and the strong-type (p,p), 1 <p < ∞, and weak-type (1,1)-boundedness of the operators is proved. The results generalise the work of L. K. Hua, A. Korányli and S. Vagi, W. Rudin and S. Gong on the Cauchy-Szegö, kemel and the Cauchy singular integral operator.

Keywords

singular integralFourier multiplierthe unit sphere in Cnlunetional calculus

Copyright information

© Science in China Press 1999

Authors and Affiliations

  • Michael Cowling
    • 1
  • Tao Qian
    • 2
  1. 1.Department of Pure MathematicsUniversity of New South WalseAustralia
  2. 2.School of Mathematical and Computer SciencesUniversity of New England ArmidaleAustralia