Higher complex Sobolev spaces on complex manifolds
Complex Variables
2025-04-14 v2 Functional Analysis
Abstract
We study higher complex Sobolev spaces and their corresponding functional capacities. In particular, we prove the Moser-Trudinger inequality for these spaces and discuss some relationships between these spaces and the complex Monge-Amp\`{e}re equation.
Cite
@article{arxiv.2405.06385,
title = {Higher complex Sobolev spaces on complex manifolds},
author = {Thai Duong Do and Duc-Bao Nguyen},
journal= {arXiv preprint arXiv:2405.06385},
year = {2025}
}
Comments
to appear in Indiana University Mathematics Journal