163841 20251107115329.0 doi 10.4153/S0008414X25101624 sideral 145836 ART-2025-145836 eng Alonso-Gutiérrez, David Universidad de Zaragoza (orcid)0000-0003-1256-3671 A discrete approach to Zhang’s projection inequality 2025 In this paper we will provide a new proof of the fact that for any convex body $K\subseteq\R^n$ $$ \frac{{{2n}\choose{n}}}{n^n}n\int_0^\infty r^{n-1}\vol_n(K\cap(re_n+K))dr\leq\frac{(\vol_n(K))^{n+1}}{(\vol_{n-1}(P_{e_n^\perp}(K)))^n}, $$ where $(e_i)_{i=1}^n$ denotes the canonical orthonormal basis in $\R^n$, $P_{e_n^\perp}(K)$ denotes the orthogonal projection of $K$ onto the linear hyperplane orthogonal to $e_n$, and $\vol_k$ denotes the $k$-dimensional Lebesgue measure. This inequality was proved by Gardner and Zhang and it implies Zhang's inequality. We will use our new approach to this inequality in order to prove discrete analogues of this inequality and of an equivalent version of it, where we will consider the lattice point enumerator measure instead of the Lebesgue measure, and show that from such discrete analogues we can recover the aforementioned inequality and, therefore, Zhang's inequality. Access copy available to the general public Unrestricted info:eu-repo/grantAgreement/ES/DGA/E48-23R info:eu-repo/grantAgreement/ES/MICINN/PID2022-137294NB-I00 info:eu-repo/semantics/openAccess by https://creativecommons.org/licenses/by/4.0/deed.es info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Lucas Marín, Eduardo Martín Goñi, Javier 2006 015 Universidad de Zaragoza Dpto. Matemáticas Área Análisis Matemático (2025), [47 pp.] Can. j. math. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES 0008-414X 685791 http://zaguan.unizar.es/record/163841/files/texto_completo.pdf Versión publicada 1647411 http://zaguan.unizar.es/record/163841/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:163841 articulos driver 2025-11-07-10:25:47 ARTICLE