English

Composition and Volterra type operators on large Bergman spaces with rapidly decreasing weights

Functional Analysis 2025-07-23 v1 Complex Variables

Abstract

We characterize boundedness, compactness and Schatten class properties of generalized Volterra-type integral operators acting between large Bergman spaces AωpA_\omega^p and AωqA_\omega^q for 0<p,q0 <p, q\leq \infty. To prove our characterizations, which involve Berezin-type integral transforms, we use the Littlewood-Paley formula of Constantin and Pel\'aez and corresponding embedding theorems. Our results generalize the work on integration operators of Pau and Pel\'{a}ez in J. Funct. Anal. 259 (2010), 2727--2756.

Keywords

Cite

@article{arxiv.2507.16437,
  title  = {Composition and Volterra type operators on large Bergman spaces with rapidly decreasing weights},
  author = {M. Almoka and H. Arroussi and J. Virtanen},
  journal= {arXiv preprint arXiv:2507.16437},
  year   = {2025}
}