000163841 001__ 163841
000163841 005__ 20251107115329.0
000163841 0247_ $$2doi$$a10.4153/S0008414X25101624
000163841 0248_ $$2sideral$$a145836
000163841 037__ $$aART-2025-145836
000163841 041__ $$aeng
000163841 100__ $$0(orcid)0000-0003-1256-3671$$aAlonso-Gutiérrez, David$$uUniversidad de Zaragoza
000163841 245__ $$aA discrete approach to Zhang’s projection inequality
000163841 260__ $$c2025
000163841 5060_ $$aAccess copy available to the general public$$fUnrestricted
000163841 5203_ $$aIn 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.
000163841 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E48-23R$$9info:eu-repo/grantAgreement/ES/MICINN/PID2022-137294NB-I00
000163841 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttps://creativecommons.org/licenses/by/4.0/deed.es
000163841 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000163841 700__ $$aLucas Marín, Eduardo
000163841 700__ $$aMartín Goñi, Javier
000163841 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático
000163841 773__ $$g(2025), [47 pp.]$$pCan. j. math.$$tCANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES$$x0008-414X
000163841 8564_ $$s685791$$uhttps://zaguan.unizar.es/record/163841/files/texto_completo.pdf$$yVersión publicada
000163841 8564_ $$s1647411$$uhttps://zaguan.unizar.es/record/163841/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000163841 909CO $$ooai:zaguan.unizar.es:163841$$particulos$$pdriver
000163841 951__ $$a2025-11-07-10:25:47
000163841 980__ $$aARTICLE