Annali di Matematica Pura ed Applicata

, Volume 165, Issue 1, pp 369–394

A martingale proof of L2 boundedness of Clifford-valued singular integrals

  • G. I. Gaudry
  • R. Long
  • T. Qian
Article

DOI: 10.1007/BF01765857

Cite this article as:
Gaudry, G.I., Long, R. & Qian, T. Annali di Matematica pura ed applicata (1993) 165: 369. doi:10.1007/BF01765857

Summary

This paper presents a theory of Clifford algebra-valued martingales on a σ-finte measure space, with respect to a pseudoaccretive weight. A novel dual pair system of Haar functions associated with the Clifford martingale is constructed, and Littlewood-Paley estimates are established. The dual pair system of Clifford Haar functions is used to give a new proof of the boundedness of the Cauchy principal value integral on Lipschitz surfaces, and of the Clifford-valued T(b) theorem.

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1993

Authors and Affiliations

  • G. I. Gaudry
    • 1
  • R. Long
    • 1
  • T. Qian
    • 1
  1. 1.Mathematics Discipline, School of Information Science and TechnologyThe Flinders University of South AustraliaAdelaide S.A.Australia

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