2024/05/23 by Athanasios Beslikas, Beslikas, Athanasios
Decision Sciences · Mathematics · #32A37 #Advanced Topics in Algebra #Complex Variables (math.CV) #FOS: Mathematics #Fuzzy and Soft Set Theory #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2405.14423
openalex publication_date 2024/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we give a new sufficient condition for the boundedness of the composition operator on the Dirichlet-type space on the disc, via a two dimensional change of variables formula. With the same formula, we characterise the bounded composition operators on the anisotropic Dirichlet-type spaces \mathfrakD_a(\mathbbD2) induced by holomorphic self maps of the bidisc \mathbbD2 of the form Φ(z1,z2)=(ϕ1(z1),ϕ2(z2)). We also consider the problem of boundedness of composition operators CΦ:\mathfrakD(\mathbbD2)→ A2(\mathbbD2) for general self maps of the bidisc, applying some recent results about Carleson measures on the the Dirichlet space of the bidisc.