Weak and strong moments of $\ell _r$-norms of log-concave vectors

Rafał Latała, Marta Strzelecka
2016 Proceedings of the American Mathematical Society  
We show that for $p\geq 1$ and $r\geq 1$ 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.
doi:10.1090/proc/13003 fatcat:y2mg5klbjzg4haifqkthn7ffie