Bergman projection and BMO in hyperbolic metric -- improvement of classical result

2022/07/03 by José Ángel Peláez, Jouni Rättyä, Peláez, José Ángel +1
Mathematics · Medicine · #30H20 #30H35 #47B34 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Sympathectomy and Hyperhidrosis Treatments

paper · pdf · doi:10.48550/arxiv.2207.01086

openalex publication_date 2022/07/03 · openalex created_date 2022/07/07 · openalex updated_date 2026/07/28

Abstract

The Bergman projection P_α, induced by a standard radial weight, is bounded and onto from L^∞ to the Bloch space B. However, P_α: L^∞→ B is not a projection. This fact can be emended via the boundedness of the operator P_α:BMO₂(Δ)\toB, where BMO₂(Δ) is the space of functions of bounded mean oscillation in the Bergman metric. We consider the Bergman projection P_ω and the space BMO_ω,p(Δ) of functions of bounded mean oscillation induced by 1

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