Pure and Applied Mathematics Quarterly

Volume 18 (2022)

Number 2

Special issue in honor of Joseph J. Kohn on the occasion of his 90th birthday

Guest Editors: J.E. Fornaess, Stanislaw Janeczko, Duong H. Phong, and Stephen S.T. Yau

Sobolev estimates and duality for $\overline{\partial}$ on domains in $\mathbb{CP}^n$

Pages: 503 – 529

DOI: https://dx.doi.org/10.4310/PAMQ.2022.v18.n2.a7


Siqi Fu (Department of Mathematical Sciences, Rutgers University, Camden, New Jersey, U.S.A.)

Mei-Chi Shaw (Department of Mathematics, University of Notre Dame, Indiana, U.S.A.)


We study $L^2$ and Sobolev estimates for solutions of the Cauchy–Riemann equation on pseudoconvex and pseudoconcave domains in $\mathbb{CP}^n$. We also formulate the weak and strong extensions of the $\overline{\partial}$ equation in Sobolev spaces and study their dual problems.


complex projective spaces, the Cauchy–Riemann operator

2010 Mathematics Subject Classification

32W05, 35N15

The authors are supported in part by NSF grants.

Received 1 March 2021

Accepted 22 April 2021

Published 13 May 2022