Bounded Functions in Mِbius Invariant Dirichlet Spaces

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∞)).