Monotonicity of functionals associated to product measures via their Fourier transform and applications

Abstract Let be a probability measure on . We give conditions on the Fourier transform of its density for functionals of the form to be Schur monotone. As applications, we put certain known and new results under the same umbrella, given by a condition on the Fourier transform of the density. These results include certain moment comparisons for independent and identically distributed random vectors, when the norm is given by intersection bodies, and vector‐valued analogues of Khinchin's inequality with respect to appropriate norms. We also extend the discussion to higher dimensions.