Asymptotic behaviour of the Teoplitz determinant

The paper deals with asymptotic behaviour of the Teoplitz determinant $D_n(f)$ for nonnegative functions $f(\lambda)$, $\lambda\in[\pi,\pi]$ Under some conditions on function $f(\lambda)$ the asymptotic representation
$$ \ln\frac{D_n(f)}{[G(f)]^{n+1}}=0(n^{-\lambda}),\quad0<\alpha<1, $$
is obtained.