L2 (k=0) extension of Sobolev solvability results on pseudoconcave domains

Establish whether the solvability and extension results for the ∂̄-equation on pseudoconcave domains Ω^+ ⊂ CP^n with Lipschitz boundary, proved in Sobolev spaces W^k for k ≥ 1 (namely Theorem W^kExistence and Theorem (n−1)-forms), remain valid in the L^2 setting when k = 0.

Background

Section 4 establishes Sobolev estimates and ∂̄-solvability on pseudoconcave domains Ω^+ with Lipschitz boundary for orders k ≥ 1, including extension results and closed range properties for the critical degree q = n − 1 under compatibility conditions.

The authors explicitly note that it is still open whether these W^k (k ≥ 1) results extend to k = 0, i.e., the L^2 case, which would complete the L^2 theory for pseudoconcave domains.