We derive sharp lower bounds for Lp-functions on the n-dimensional unit hypercube in terms of their p-ths marginal moments. Such bounds are the unique solutions of a system of constrained nonlinear integral equations depending on the marginals. For square-integrable functions, the bounds have an explicit expression in terms of the second marginals moments.
Guasoni P, Mayerhofer E, Zhao M (2021). Minimal L-p-densities with prescribed marginals. BERNOULLI, 27(1), 576-585 [10.3150/20-BEJ1250].
Minimal L-p-densities with prescribed marginals
Guasoni PCo-primo
;
2021
Abstract
We derive sharp lower bounds for Lp-functions on the n-dimensional unit hypercube in terms of their p-ths marginal moments. Such bounds are the unique solutions of a system of constrained nonlinear integral equations depending on the marginals. For square-integrable functions, the bounds have an explicit expression in terms of the second marginals moments.File in questo prodotto:
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