Let K(x,t) be a positive definite Hermitian \(C^ p\) kernel on \(| x| \leq 1\), \(| t| \leq 1\); and \(e_ 1\geq e_ 2\geq...\geq e_ n\geq..\). the associated eigenvalues. \textit{Chungwei Ha} [ibid. 17, 415-419 (1986; reviewed above)] has proved recently that, for p even, \(\sum_{n\geq 1}n^ pe_ n<+\infty.\) In this paper, the author proves that this result is false for p odd, by the following counterexample: \[ K(x,t)=\sum_{n\geq 1}e_ n\cos (\pi nx)\cos (\pi nt),\quad \sum_{n\geq 1}e^ 2_ n<\infty. \]