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PreprintarXiv licencearXiv

Volterra operators on the BMOA space of Dirichlet series

  • Cezhong Tong
  • Maofa Wang
  • Zixing Yuan
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Abstract

In this paper, we completely characterize the boundedness and compactness of Volterra operators on BMOAπ’Ÿ, the BMOA space of Dirichlet series, and estimate their essential and weak essential norms. We further prove that compactness, weak compactness, and complete continuity are equivalent for these operators. In particular, every Dirichlet polynomial symbol induces a compact Volterra operator on BMOAπ’Ÿ. We also prove that every such symbol induces a compact Volterra operator on the Bergman space of Dirichlet series π’œΞΌ1 for every admissible measure ΞΌ, extending the corresponding compactness theorem, previously established for 1<p<∞, to the endpoint p=1.

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Cite

BibTeXRIS
BibTeX
@misc{tong2026volterra,
  title = {{Volterra operators on the BMOA space of Dirichlet series}},
  author = {Cezhong Tong and Maofa Wang and Zixing Yuan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.21873},
  eprint = {2610.21873},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.21873},
}
RIS
TY  - UNPB
TI  - Volterra operators on the BMOA space of Dirichlet series
AU  - Cezhong Tong
AU  - Maofa Wang
AU  - Zixing Yuan
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.21873
UR  - https://arxiv.org/abs/2610.21873
AB  - In this paper, we completely characterize the boundedness and compactness of Volterra operators on BMOA_π’Ÿ, the BMOA space of Dirichlet series, and estimate their essential and weak essential norms. We further prove that compactness, weak compactness, and complete continuity are equivalent for these operators. In particular, every Dirichlet polynomial symbol induces a compact Volterra operator on BMOA_π’Ÿ. We also prove that every such symbol induces a compact Volterra operator on the Bergman space of Dirichlet series π’œ_ΞΌ^1 for every admissible measure ΞΌ, extending the corresponding compactness theorem, previously established for 1<p<∞, to the endpoint p=1.
ER  -