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Let ψ and φ be analytic functions on the open unit disk with φ() ⊆ . We give new characterizations of the bounded and compact weighted composition operators W ψ,ϕ from the Hardy spaces H p, 1 ≤ p ≤ ∞, the Bloch space B, the weighted Bergman spaces A αp, α > − 1,1 ≤ p < ∞, and the Dirichlet space to the Bloch space in terms of boundedness (respectively, convergence to 0) of the Bloch norms of W ψ,ϕ f for suitable collections of functions f in the respective spaces. We also obtain characterizations...
In this paper we study the Radon transform on the set of horocycles of a homogeneous tree , and describe its image on various function spaces. We show that the functions of compact support on that satisfy two explicit constitute the image under of functions of finite support on . We extend these results to spaces of functions with suitable decay on , whose image under satisfies corresponding decay conditions and contains distributions on that are not defined pointwise. We also show...
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