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.
N. Arcozzi, R. Rochberg, E. Sawyer (2008). Capacity, Carleson measures, boundary convergence, and exceptional sets. PROVIDENCE RI : American Mathematical Society.
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:
Eventuali allegati, non sono esposti
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
