We propose to study the potential theory of the signed Riesz kernels R (x) = x/(|x|1+). This corresponds, in accordance with the classical point of view of Calderón-Zygmund Theory, to consider dimensional real variables versions of the striking results obtained recently for the Cauchy kernel in the plane. Specifically, we would like to deal with the problem, raised by David and Semmes, of characterizing uniform rectifiability by means of the L2-boundedness of the operators associated to the Riesz kernels. We also would like to show that the capacity associated to Ris semiadditive. Finally we propose to develop a theory of the capacity associated to the Beltrami operator ¯@ - µ(z)@, where µk1 <1
|Effective start/end date||1/10/04 → 30/09/05|
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