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

Abstract

We show that for $p\ge 1$ and $r\ge 1$ 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.

14 pages, proof modified to include the case r<2

References in corpus (3)

• A short proof of Paouris' inequality
• Sudakov-type minoration for log-concave vectors
• Modified Paouris inequality

Cited by in corpus (4)

• Comparison of weak and strong moments for vectors with independent coordinates
• On the convex infimum convolution inequality with optimal cost function
• Hadamard products and moments of random vectors
• Estimates of norms of log-concave random matrices with dependent entries