TY - JOUR
T1 - Bounded functions in Möbius invariant Dirichlet spaces
AU - Nicolau, Artur
AU - Xiao, Jie
PY - 1997/11/1
Y1 - 1997/11/1
N2 - Forp∈(0,1), letQp(Qp,0) be the space of analytic functionsfon the unit diskΔwith supw∈Δ∥f°φw∥Dp<∞ (lim|w|→1∥f°φw∥Dp=0), where ∥·∥Dpmeans the weighted Dirichlet norm andφwis the Möbius map ofΔonto itself withφw(0)=w. In this paper, we prove the Corona theorem for the algebraQp∩H∞(Qp,0∩H∞); then we provide a Fefferman-Stein type decomposition forQp(Qp,0), and finally we describe the interpolating sequences forQp∩H∞(Qp,0∩H∞)). © 1997 Academic Press.
AB - Forp∈(0,1), letQp(Qp,0) be the space of analytic functionsfon the unit diskΔwith supw∈Δ∥f°φw∥Dp<∞ (lim|w|→1∥f°φw∥Dp=0), where ∥·∥Dpmeans the weighted Dirichlet norm andφwis the Möbius map ofΔonto itself withφw(0)=w. In this paper, we prove the Corona theorem for the algebraQp∩H∞(Qp,0∩H∞); then we provide a Fefferman-Stein type decomposition forQp(Qp,0), and finally we describe the interpolating sequences forQp∩H∞(Qp,0∩H∞)). © 1997 Academic Press.
U2 - https://doi.org/10.1006/jfan.1997.3114
DO - https://doi.org/10.1006/jfan.1997.3114
M3 - Article
SN - 0022-1236
VL - 150
SP - 383
EP - 425
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
ER -