In this paper the relation between certain "testing conditions" and "capacitary conditions" for a measure to be Carleson for the Dirichlet space are discussed, in the dyadic case. In particular, a direct proof of the equivalence of the two conditions is proved, answering a question by Maz'ya. The analysis of these conditions is then used to give a new definition of capacity and to investigate the boundary behavior of functions in the Dirichlet class.
Capacity, Carleson measures, boundary convergence, and exceptional sets
ARCOZZI, NICOLA;
2008
Abstract
In this paper the relation between certain "testing conditions" and "capacitary conditions" for a measure to be Carleson for the Dirichlet space are discussed, in the dyadic case. In particular, a direct proof of the equivalence of the two conditions is proved, answering a question by Maz'ya. The analysis of these conditions is then used to give a new definition of capacity and to investigate the boundary behavior of functions in the Dirichlet class.File in questo prodotto:
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