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Cesàro-type operators associated with Borel measures on the unit disc acting on some Hilbert spaces of analytic functions Galanopoulos, Petros Girela-Álvarez, Daniel Merchán-Álvarez, Noel Análisis matemático Given a complex Borel measure μon the unit disc D={z∈C:|z| <1}, we consider the Cesàro-type operator Cμdefined on the space Hol(D)of all analytic functions in Das follows: If f∈Hol(D), f(z) = ∞n=0anzn(z∈D), then Cμ(f)(z) = ∞n=0μn nk=0ak zn, (z∈D), where, for n ≥0, μndenotes the n-th moment of the measure μ, that is, μn= Dwndμ(w). We study the action of the operators Cμon some Hilbert spaces of analytic function in D, namely, the Hardy space H2and the weighted Bergman spaces A2α(α >−1). Among other results, we prove that, if we set Fμ(z) = ∞n=0μnzn(z∈D), then Cμis bounded on H2or on A2αif and only if Fμbelongs to the mean Lipschitz space Λ21/2. We prove also that Cμis a Hilbert-Schmidt operator on H2if and only if Fμbelongs to the Dirichlet space D, and that Cμis a Hilbert-Schmidt operator on A2αif and only if Fμbelongs to the Dirichlet-type space D2−1−α. 2023-04-21T09:47:32Z 2023-04-21T09:47:32Z 2023 journal article Petros Galanopoulos, Daniel Girela, Noel Merchán, Cesàro-type operators associated with Borel measures on the unit disc acting on some Hilbert spaces of analytic functions, Journal of Mathematical Analysis and Applications, Volume 526, Issue 2, 2023, 127287, ISSN 0022-247X, https://doi.org/10.1016/j.jmaa.2023.127287. (https://www.sciencedirect.com/science/article/pii/S0022247X23002901) https://hdl.handle.net/10630/26343 https://doi.org/10.1016/j.jmaa.2023.127287 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Elsevier