Norm-attaining integral operators on analytic function spaces

2012/03/22 by Chengji Xiong, Xiong, Chengji, Junming Liu +2
Mathematics · #30H #45P05 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV #msc:30H #msc:45P05

paper · pdf · doi:10.48550/arxiv.1203.4904

9 pages

arxiv created 2012/03/22 · openalex publication_date 2012/03/22 · arxiv updated 2012/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Any bounded analytic function g induces a bounded integral operator S_g on the Bloch space, the Dirichlet space and BMOA respectively. S_g attains its norm on the Bloch space and BMOA for any g, but does not attain its norm on the Dirichlet space for non-constant g. Some results are also obtained for S_g on the little Bloch space, and for another integral operator T_g from the Dirichlet space to the Bergman space.

Citations

• The Q p Carleson measure problem

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