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.
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Research supported by the Australian Research Council.
Research supported by the National Science Foundation of China.
Research carried out as a National Research Fellow.
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Gaudry, G.I., Long, R. & Qian, T. A martingale proof of L2 boundedness of Clifford-valued singular integrals. Annali di Matematica pura ed applicata 165, 369–394 (1993). https://doi.org/10.1007/BF01765857
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DOI: https://doi.org/10.1007/BF01765857