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Let B n p = {(x i ) E R n ; Σ n 1 |x i | p < 1} and let E be a k-dimensional subspace of R n . We prove that |E ∩ B n p | 1/k k ≥ |B n p | 1/n n , for 1 ≤ k ≤ (n - 1)/2 and k = n - 1 whenever 1 < p < 2. We also consider 0 < p < 1 and other related cases. We obtain sharp inequalities involving Gamma function in order to get these results.

Inequalities for the Gamma function and estimates for the volume of sections of $B^n_p$