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We provide necessary and sufficient conditions for hypercontractivity of theminima of nonnegative, i.i.d. random variables and of both the maxima ofminima and the minima of maxima for such r.v.'s. It turns out that the idea ofhypercontractivity for minima is closely related to small ball probabilitiesand Gaussian correlation inequalities.

Hypercontractivity and Comparison of Moments of Iterated Maxima and Minima of Independent Random Variables