Holder's inequality and its reverse-A probabilistic point of view

In this article, we take a probabilistic look at Holder's inequality, considering the ratio of terms in the classical Holder inequality for random vectors in R-n. We prove a central limit theorem for this ratio, which then allows us to reverse the inequality up to a multiplicative constant with high probability. The models of randomness include the uniform distribution on l(p)(n). balls and spheres. We also provide a Berry-Esseen-type result and prove a large and a moderate deviation principle for the suitably normalized Holder ratio.