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New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space

Flavia Colonna — 2013

Open Mathematics

Let ψ and φ be analytic functions on the open unit disk 𝔻 with φ( 𝔻 ) ⊆ 𝔻 . 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 𝒟 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...

Range of the horocyclic Radon transform on trees

Enrico Casadio Tarabusi;  Joel M. Cohen;  Flavia Colonna — 2000

Annales de l'institut Fourier

In this paper we study the Radon transform R on the set ℋ of horocycles of a homogeneous tree T , and describe its image on various function spaces. We show that the functions of compact support on ℋ that satisfy two explicit constitute the image under R of functions of finite support on T . We extend these results to spaces of functions with suitable decay on T , whose image under R satisfies corresponding decay conditions and contains distributions on ℋ that are not defined pointwise. We also show...

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