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Corona and Gleason problems for certain Banach spaces of holomorphic functions

  • S. R. Patel
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Abstract

We use a combination of the classical dead-end space method and the interpolation (by bounded holomorphic functions) method to affirmatively solve Corona and Gleason problems for familiar Banach spaces of holomorphic functions such as (Besov-)Lipschitz spaces of holomorphic functions on bounded symmetric domains (including the unit ball and polydisc) in ℂn, holomorphic mean (Besov-)Lipschitz spaces, (Besov-)Hardy-Sobolev spaces and some special classes of holomorphic mixed-norm (Bergman) spaces (including weighted Bergman spaces) as well as some special classes of holomorphic (mean) Besov-Lipschitz spaces on the unit ball in ℂn. Indeed, we extend our recent work on both problems for holomorphic Lipschitz algebras.

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Cite

BibTeXRIS
BibTeX
@misc{patel2026corona,
  title = {{Corona and Gleason problems for certain Banach spaces of holomorphic functions}},
  author = {S. R. Patel},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02949},
  eprint = {2611.02949},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02949},
}
RIS
TY  - UNPB
TI  - Corona and Gleason problems for certain Banach spaces of holomorphic functions
AU  - S. R. Patel
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.02949
UR  - https://arxiv.org/abs/2611.02949
AB  - We use a combination of the classical dead-end space method and the interpolation (by bounded holomorphic functions) method to affirmatively solve Corona and Gleason problems for familiar Banach spaces of holomorphic functions such as (Besov-)Lipschitz spaces of holomorphic functions on bounded symmetric domains (including the unit ball and polydisc) in ℂ^n, holomorphic mean (Besov-)Lipschitz spaces, (Besov-)Hardy-Sobolev spaces and some special classes of holomorphic mixed-norm (Bergman) spaces (including weighted Bergman spaces) as well as some special classes of holomorphic (mean) Besov-Lipschitz spaces on the unit ball in ℂ^n. Indeed, we extend our recent work on both problems for holomorphic Lipschitz algebras.
ER  -