Saint Petersburg State University, Russia
Date(s) : 09/04/2018 iCal
10 h 00 min - 11 h 00 min
The Dirichlet space on the polydisc Dd,d≥1, consists of analytic functions satisfying . In the one-dimensional case (d=1) the Carleson measures were first described by Stegenga (’80) in terms of capacity, further development was achieved in papers by Arcozzi, Rochberg, Sawyer, Wick and others. Following Arcozzi et al. we consider the equivalent problem in the discrete setting — characterization of trace measures for the Hardy operator on the polytree Td. For d=2 we present a description of such measures in terms of bilogarithmic capacity (which, in turn, gives the description of Carleson measures for (D2) in the sense of Stegenga). We also discuss some arising combinatorial problems. This talk is based on joint work with N. Arcozzi, K.-M. Perfekt, G. Sarfatti.