RT Journal Article
T1 Operators induced by radial measures acting on the Dirichlet space
A1 Galanopoulos, Petros
A1 Girela-Álvarez, Daniel
A1 Mas, Alejandro
A1 Merchán-Álvarez, Noel
K1 Análisis funcional
K1 Análisis matemático
AB 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<∞).
PB Springer
YR 2023
FD 2023
LK https://hdl.handle.net/10630/26379
UL https://hdl.handle.net/10630/26379
LA eng
NO 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
NO Funding for open access publishing: Universidad Málaga/CBUA .This research is supported in part by a grant from “El Ministerio de Economía y Competitividad”, Spain (PGC2018-096166-B-I00 and PID2019-106870GB 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 21 ene 2026