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analytic capacity

Proceedings of the London Mathematical Society (1)

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Riesz transforms and harmonic Lip1-capacity in Cantor sets
Joan Mateu, Xavier Tolsa
Journal:

Proceedings of the London Mathematical Society / Volume 89 / Issue 3 / November 2004

Published online by Cambridge University Press:

05 November 2004, pp. 676-696

Print publication:

November 2004
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We estimate the $L^2$-norm of the $s$-dimensional Riesz transforms on some Cantor sets in ${\mathbb R}^d$. 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.