We estimate the L2-norm of the s-dimensional Riesz transforms on some Cantor sets in Rd. Towards this end, we show that the Riesz transforms truncated at different scales behave in a quasiorthogonal way. As an application, we obtain some precise numerical estimates for the Lipschitz harmonic capacity of these sets. 2000 Mathematics Subject Classification 42B20, 42B25.
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Mateu et al. (2004) studied this question.
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