Bounded functions in Möbius invariant Dirichlet spaces

Artur Nicolau, Jie Xiao

Research output: Contribution to journalArticleResearchpeer-review

44 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)383-425
JournalJournal of Functional Analysis
Volume150
DOIs
Publication statusPublished - 1 Nov 1997

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