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.
Minimal L-p-densities with prescribed marginals / Guasoni P; Mayerhofer E; Zhao M. - In: BERNOULLI. - ISSN 1350-7265. - STAMPA. - 27:1(2021), pp. 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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