A Weighted Prékopa–Leindler Inequality and Sumsets with Quasicubes

Ben Green (), Dávid Matolcsi, Imre Ruzsa, George Shakan and Dmitrii Zhelezov
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Ben Green: University of Oxford
Dávid Matolcsi: Eötvös Loránd University
Imre Ruzsa: Rényi Institute of Mathematics
George Shakan: Centre de Recherches Mathématiques
Dmitrii Zhelezov: Radon Institute for Computational and Applied Mathematics RICAM

A chapter in Analysis at Large, 2022, pp 125-129 from Springer

Abstract: Abstract We give a short, self-contained proof of two key results from a paper of four of the authors. The first is a kind of weighted discrete Prékopa–Leindler inequality. This is then applied to show that if A , B ⊆ ℤ d $$A, B \subseteq \mathbb {Z}^d$$ are finite sets and U is a subset of a “quasicube”, then | A + B + U | ⩾ | A | 1 ∕ 2 | B | 1 ∕ 2 | U | $$|A + B + U| \geqslant |A|{ }^{1/2} |B|{ }^{1/2} |U|$$ . This result is a key ingredient in forthcoming work of the fifth author and Pälvölgyi on the sum-product phenomenon.

Keywords: Primary; 11B30 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-05331-3_6

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DOI: 10.1007/978-3-031-05331-3_6

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