Abstract. We show that a maximal inequality holds for the non-tangential maximal operator on Dirichlet spaces with harmonic weights on the open unit disc. We then investigate two notions of Carleson measures on these spaces and use the maximal inequality to give characterizations of the Carleson measures in terms of an associated capacity.
Abstract. In this paper we study composition operators on spaces of entire functions. We determine which entire functions induce bounded composition operators on the Paley-Wiener space, L 2 π , and on the E 2 (γ) spaces. In addition, we characterize compact composition operators on these spaces. We also study the cyclic properties of composition operators acting on L 2 π .
In this article we show that interpolating sequences on certain harmonically weighted Dirichlet spaces can be characterized in terms of a separation condition and a Carleson-measure condition. This is the first example of a space with Nevanlinna-Pick kernel with non-radially symmetric weights in which this characterization remains true.Mathematics Subject Classification (2010). Primary 30E05; Secondary 40E20.
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