arXiv subjects
Publications and source records attributed to E. Sawyer.
We investigate connections between potential theories on a Ahlfors-regular metric space X, on a graph G associated with X, and on the tree T obtained by removing the "horizontal edges" in G. Applications to the calculation of set capacity are given.
We give a simple proof of the characterization of the Carleson measures for the weighted analytic Besov spaces. Such characterization provides some information on the radial variation of an analytic Besov function.
We characterize the Carleson measures for the Drury-Arveson Hardy space and other Hilbert spaces of analytic functions of several complex variables. This provides sharp estimates for Drury's generalization of Von Neumann's inequality. The characterization is in terms of a geometric condition, the "split tree condition", which reflects the nonisotropic geometry underlying the Drury-Arveson Hardy space.