A class of symbols that induce bounded composition operators for Dirichlet-type spaces on the disc

Athanasios Beslikas

doi:10.1017/S0004972724000170

A class of symbols that induce bounded composition operators for Dirichlet-type spaces on the disc

Complex Variables 2025-02-19 v2

Authors: Athanasios Beslikas

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

In this note we study the problem of determining the holomorphic self maps of the unit disc that induce a bounded composition operator on Dirichlet-type spaces. We find a class of symbols $\varphi$ that induce a bounded composition operator on the Dirichlet-type spaces, by applying results of the multidimensional theory of composition operators for the weighted Bergman spaces of the bi-disc.

Keywords

composition operators dirichlet-type spaces holomorphic self maps weighted bergman spaces bi-disc bounded operators symbol class

Cite

@article{arxiv.2402.10759,
  title  = {A class of symbols that induce bounded composition operators for Dirichlet-type spaces on the disc},
  author = {Athanasios Beslikas},
  journal= {arXiv preprint arXiv:2402.10759},
  year   = {2025}
}

Comments

5 pages, accepted for publication in Bulletin of Australian Mathematical Society

Related papers

View all related →