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Riesz Transforms and Harmonic Lip 1 ‐Capacity in Cantor Sets
Author(s) -
Mateu Joan,
Tolsa Xavier
Publication year - 2004
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611504014790
Subject(s) - mathematics , riesz transform , riesz representation theorem , lipschitz continuity , riesz potential , m. riesz extension theorem , norm (philosophy) , pure mathematics , mathematics subject classification , harmonic , mathematical analysis , physics , quantum mechanics , political science , law
We estimate the L 2 ‐norm of the s ‐dimensional Riesz transforms on some Cantor sets in 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. 2000 Mathematics Subject Classification 42B20, 42B25.