Let \(K=\{x\in R^ m:| x_ i| \leq \pi\), \(i=1,2,...,m\}\) and the \(2\pi\)-periodic function f(x), \(x\in K\) have a unique singularity point \(x_ 0\). If \(x_ 0=0\) then there is some non-negative decreasing function \(\alpha\) (u) on (0,T] such that \(\| x\|^{\alpha (\| x\|)}f(x)\in L(K).\) Let M(u) be an integer-valued non-negative function on (0,T] satisfying M(u)\(\geq \alpha (u)\), \(0