RT Journal Article
T1 Compostion of Analytic Paraproducts
A1 Aleman, Alexandru
A1 Cascante, Carmen
A1 Fàbrega, Joan
A1 Pascuas, Daniel
A1 Peláez-Márquez, José Ángel
K1 Hardy, Espacios de
AB For a fixed  analytic function $g$ on the unit disc $\D$, we consider the analytic paraproducts induced by $g$, which are defined by $T_gf(z)= \int_0^z f(\z)g'(\z)\,d\z$,$S_gf(z)= \int_0^z f'(\z)g(\z)\,d\z$, and$M_gf(z)= f(z)g(z)$.  The boundedness of these operators on various spaces of analytic functions on $\D$ is well understood. The original motivation for this work is to understand the boundedness of compositions of two of these operators, for example $T_g^2, \,T_gS_g,\,  M_gT_g$, etc. Our methods yield a characterization of the  boundedness    of a large class of operators contained in  the algebra generated by these  analytic paraproducts acting on the classical weighted Bergman and Hardy spaces in terms of the symbol $g$. In some cases it turns out that this property is not  affected by cancellation, while in others it requires stronger and more subtle restrictions on the oscillation of the symbol $g$ than  the case of a single paraproduct.
PB Elsevier
YR 2022
FD 2022
LK https://hdl.handle.net/10630/37198
UL https://hdl.handle.net/10630/37198
LA eng
NO Alexandru Aleman, Carme Cascante, Joan Fàbrega, Daniel Pascuas, José Ángel Peláez, Composition of analytic paraproducts, Journal de Mathématiques Pures et Appliquées, Volume 158, 2022, Pages 293-319, ISSN 0021-7824, https://doi.org/10.1016/j.matpur.2021.11.007. (https://www.sciencedirect.com/science/article/pii/S0021782421001689)
NO The research of the second, third and fourth author was supported in part by        Ministerio de Economía y Competitividad, Spain,   project  MTM2017-83499-P,  and Generalitat de Catalunya, project2017SGR358.The research of the fifth author was supported in part by Ministerio de Economíaa y Competitividad, Spain, projectsPGC2018-096166-B-100; La Junta de Andalucía, projects FQM210  and UMA18-FEDERJA-002.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026