2026-06-02T13:08:24Zhttps://riuma.uma.es/rest/oai/request

oai:riuma.uma.es:10630/263792026-02-03T11:09:58Zcom_10630_2254col_10630_37953

Galanopoulos, Petros Girela-Álvarez, Daniel Mas, Alejandro Merchán-Álvarez, Noel 2023-04-24T08:56:12Z 2023-04-24T08:56:12Z 2023 Galanopoulos, P., Girela, D., Mas, A. et al. Operators Induced by Radial Measures Acting on the Dirichlet Space. Results Math 78, 106 (2023). https://doi.org/10.1007/s00025-023-01887-6 https://hdl.handle.net/10630/26379 https://doi.org/10.1007/s00025-023-01887-6 Let D be the unit disc in the complex plane. Given a positive finite Borel measure μ on the radius [0, 1), we let μn denote the n-th moment of μ and we deal with the action on spaces of analytic functions in D of the operator of Hibert-type Hμ and the operator of Cesàro-type Cμ which are defined as follows: If f is holomorphic in D, f(z)=∑∞n=0anzn (z∈D), then Hμ(f) is formally defined by Hμ(f)(z)=∑∞n=0(∑∞k=0μn+kak)zn (z∈D) and Cμ(f) is defined by Cμ(f)(z)=∑∞n=0μn(∑nk=0ak)zn (z∈D ). These are natural generalizations of the classical Hilbert and Cesàro operators. A good amount of work has been devoted recently to study the action of these operators on distinct spaces of analytic functions in D. In this paper we study the action of the operators Hμ and Cμ on the Dirichlet space D and, more generally, on the analytic Besov spaces Bp (1≤p<∞). eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Análisis funcional Análisis matemático Operators induced by radial measures acting on the Dirichlet space journal article