PreprintarXiv licencearXiv
Strongly Pseudoconvex Domains with Finite Dimensional p-Bergman Spaces
Abstract
We show that for every n≥2, p>2, and positive integer m, there exists a finite-volume pseudoconvex domain D⊂ℂn with real-analytic strongly pseudoconvex boundary whose p-Bergman space Ap(D) has dimension m. These domains admit smooth strictly plurisubharmonic exhaustions and satisfy H∞(D)=ℂ and dim As(D)=∞ for every 0<s≤2. Moreover, for every finite s≥ p, we have dim As(D)=⌈ pm/s⌉. As an application, we show that the Bergman projection fails to map 𝒞c∞(D) into Ap(D) and admits no bounded extension to Ls(D) or Ls/(s−1)(D) for any finite s≥ p.
Related
- Pseudoconvex domains in complex Euclidean space with finite-dimensional Bergman spaces
- CSC Bergman metrics are Einstein on pseudoconvex domains
- Comparison of the Bergman and Szegő kernels on arbitrary bounded pseudoconvex domains with C2 boundary
- Rigidity of Extremal and cscK Bergman Metrics on Pseudoconvex Domains
- Kobayashi completeness of pseudoconvex domains: finite type and a smooth counterexample
BibTeX
@misc{bhat2026strongly,
title = {{Strongly Pseudoconvex Domains with Finite Dimensional $p$-Bergman Spaces}},
author = {Shreedhar Bhat and Soumya Ganguly and Achinta Kumar Nandi},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00501},
eprint = {2611.00501},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00501},
}
RIS
TY - UNPB
TI - Strongly Pseudoconvex Domains with Finite Dimensional p-Bergman Spaces
AU - Shreedhar Bhat
AU - Soumya Ganguly
AU - Achinta Kumar Nandi
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00501
UR - https://arxiv.org/abs/2611.00501
AB - We show that for every n≥2, p>2, and positive integer m, there exists a finite-volume pseudoconvex domain D⊂ℂ^n with real-analytic strongly pseudoconvex boundary whose p-Bergman space A^p(D) has dimension m. These domains admit smooth strictly plurisubharmonic exhaustions and satisfy H^∞(D)=ℂ and dim A^s(D)=∞ for every 0<s≤2. Moreover, for every finite s≥ p, we have dim A^s(D)=⌈ pm/s⌉. As an application, we show that the Bergman projection fails to map 𝒞_c^∞(D) into A^p(D) and admits no bounded extension to L^s(D) or L^s/(s−1)(D) for any finite s≥ p.
ER -