Berry-Esseen bounds in central limit theorem for transport distances

For sums of independent random variables $S_n=X_1+\dots+X_n$, Berry-Esseen-type bounds are derived for the transport power distances $W_p$ in terms of Lyapunov coefficients $L_{p+2}$. These bounds extend the results by E. Rio from the range $1 < p\le 2$ to all values $p >1$.