2019/01/31 by A. -K. Gallagher, A.-K. Gallagher, J. Lebl +1
Mathematics · #Advanced Harmonic Analysis Research #Differential geometry #Fourier analysis #Geometry and complex manifolds #Holomorphic and Operator Theory #Planar #Property (philosophy) #Range (aeronautics) #Space (punctuation) #math.AP #math.CV #msc:31A15 #msc:32W05
paper · pdf · doi:10.1007/s12220-019-00318-9
published as J. Geom. Anal., 31 (2021), 1646-1670 · Part (iv) of Proposition 2.2 in the previous version was stated prematurely. To correct this, some changes in section 2 were necessary, see Prop. 2.9 and its corollaries in the current version
openalex created_date 2019/01/25 · arxiv created 2019/10/29 · openalex publication_date 2019/11/13 · arxiv updated 2021/02/17 · openalex updated_date 2026/08/05
Let Ω⊂ℂ be an open set. We show that ∂ has closed range in L2(Ω) if and only if the Poincaré-Dirichlet inequality holds. Moreover, we give necessary and sufficient potential-theoretic conditions for the ∂-operator to have closed range in L2(Ω). We also give a new necessary and sufficient potential-theoretic condition for the Bergman space of Ω to be infinite dimensional.