Weak and strong moments of l_r-norms of log-concave vectors

Rafał Latała, Marta Strzelecka

Published 2015-01-07Version 1

We show that for $p\geq 1$ and $r\geq 2$ the $p$-th moment of the $l_r$-norm of a log-concave random vector is comparable to the sum of the first moment and the weak $p$-th moment up to a constant proportional to $r$. This extends the previous result of Paouris concerning Euclidean norms.