Uniform Estimates of the Cauchy–Riemann Equation and Kerzman’s Question
Year: 2025
Type: article
Abstract: We answer a question raised by Kerzman in 1971. More precisely, we show that the canonical solution of the $${\bar{\partial }}$$ ∂ ¯ -equation satisfies the $$L^p$$ L p estimate on the polydisc for $$p \in [1, \infty ]$$ p ∈ [ 1 , ∞ ] . Moreover, the $$L^p$$ L p estimates for $$p \in [1, \infty ]$$ p ∈ [ 1 , ∞ ] of $${\bar{\partial }}$$ ∂ ¯ can also be obtained on the product of bounded $$C^2$$ C 2 planar domains by an observation based on the method developed in [Dong et al. arXiv:2006.14484].
Source: Peking Mathematical Journal
Author: Yuan Yuan
Institution: Syracuse University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4408766699