RT Journal Article
T1 Cesàro-type operators associated with Borel measures on the unit disc acting on some Hilbert spaces of analytic functions
A1 Galanopoulos, Petros
A1 Girela-Álvarez, Daniel
A1 Merchán-Álvarez, Noel
K1 Análisis matemático
AB 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.
PB Elsevier
YR 2023
FD 2023
LK https://hdl.handle.net/10630/26343
UL https://hdl.handle.net/10630/26343
LA eng
NO 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)
NO Funding for open access charge: Universidad de Málaga / CBUAThis research is supported in part by a grant from “El Ministerio de Economía y Competitividad” Spain (PGC2018-096166-B-I00) and by grants from la Junta de Andalucía (FQM-210 and UMA18-FEDERJA-002).
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026