A remark to 'Global regularity and spectra of Laplace-Beltrami operators on pseudoconvex domains' (Q1070077)

In the previous work in Publ. Res. Inst. Math. Sci. 19, 275-304 (1983; Zbl 0555.32013) the author proved the following: If D is a smooth, relatively compact pseudoconvex domain in a complex manifold M and \(B\to M\) is a positive holomorphic line bundle then for every \(0\leq s\in N\) there is an m(s)\(\in {\mathbb{Z}}\), m(s)\(\geq 0\) such that if \(m\geq m(s)\) then the equation \({\bar \partial}u=v\) always has a solution \(u\in C_ s^{p,q-1}(\bar D,B^{\otimes m})\) whenever \(v\in C_ s^{p,q}(\bar D,B^{\otimes m})\) satisfying \({\bar \partial}v=0.\) The present paper gives an example to show that we cannot always take \(m(s)=1\).