Let X be a d-dimensional standardized random variable (E(X) = 0, cov(X) = 1). Then
for a multivariate analogue of skewness s = E (parallel-to X parallel-to 2X) and kurtosis
k = EXX(T)XX(T)-(d+2)I we show that parallel-to s parallel-to 2 < tr k + 2d. For infinitely
divisible distributions parallel-to s parallel-to 2 less-than-or-equal-to tr k.
