We expand the ranges of permissible values of $n$ ($n\in\mathbb{ N}$) for which Poisson kernels $P_{ q,\beta}(t)=\sum\limits_{ k=1}^{ \infty}q^k\cos\left(kt-\dfrac{ \beta\pi}{ 2}\right)$, ${ q\in(0,1)}$, $\beta\in\mathbb{ R}$, satisfy Kushpel's condition $C_{ y,2n}$. As a consequence, we obtain exact values for Kolmogorov widths in the space $C$ ($L$) of classes $C_{ \beta,\infty}^q$ ($C_{ \beta,1}^q$) of Poisson integrals generated by kernels $P_{ q,\beta}(t)$ in new situations. It is shown that obtained here results we can't obtain by using methods of finding of exact lower bounds for widths suggested by A. Pinkus.
Categories: math.CA