Small deviations of the maximal element of a sequence of independent variables with smooth weights

We study the logarithmic small deviations of the maximal element of a sequence $\{\lambda_jX_j\}$, where $\{X_j\}$ are independent copies of non-negative random variable $X$ and $\{\lambda_j\}$ is a non-increasing sequence of positive numbers, satisfying certain conditions of regularity. Bibl. – 3 titles.