In this paper, we introduce pseudo-Carleson measure, a generalization of Carleson for Fock spaces, and give sufficient necessary conditions complex Borel measure to be pseudo-Carleson. We then integral representations functions in space, use the measures characterize boundedness compactness small Hankel operators on spaces.

There is a fundamental relation between the capacity of a set and energy integrals of probability measures supported on that set. If the capacity is small the energy integral will be large; in particular sets of capacity zero cannot support probability measures of …nite energy. Here we develop similar ideas relating capacity to Carleson measures. We show that if a set has small capacity then an...

We prove that, for every α > −1, the pull-back measure φ(Aα) of the measure dAα(z) = (α+1)(1− |z| ) dA(z), where A is the normalized area measure on the unit disk D, by every analytic self-map φ : D → D is not only an (α + 2)-Carleson measure, but that the measure of the Carleson windows of size εh is controlled by ε times the measure of the corresponding window of size h. This means that the p...

Given a bounded strongly pseudoconvex domain D in C with smooth boundary, we characterize (p, q, α)-Bergman Carleson measures for 0 < p < ∞, 0 < q < ∞, and α > −1. As an application, we show that the Bergman space version of the balayage of a Bergman Carleson measure on D belongs to BMO in the Kobayashi metric.

This is a survey on reverse Carleson measures for various Hilbert spaces of analytic functions. These spaces include the Hardy, Bergman, certain harmonically weighted Dirichlet, Paley-Wiener, Fock, model (backward shift invariant), and de Branges-Rovnyak spaces. The reverse Carleson measure for backward shift invariant subspaces in the non-Hilbert situation is new.

on the associated Bergman tree Tn. Combined with recent results about interpolating sequences this leads, for this range of σ, to a characterization of universal interpolating sequences for B 2 and also for its multiplier algebra. However, the tree condition is not necessary for a measure to be a Carleson measure for the Drury-Arveson Hardy space H n = B 1/2 2 . We show that μ is a Carleson mea...