2020
DOI: 10.1016/j.jnt.2019.07.001
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Three convolution inequalities on the real line with connections to additive combinatorics

Abstract: We discuss three convolution inequalities that are connected to additive combinatorics. Cloninger and the second author showed that for nonnegative f ∈ L 1 (−1/4, 1/4),which is related to g−Sidon sets (1.28 cannot be replaced by 1.52). We prove a dual statement, related to difference bases, and show that for f ∈ L 1 (R),where the constant 1/2 is trivial, 0.42 cannot be replaced by 0.37. This suggests a natural conjecture about the asymptotic structure of g−difference bases. Finally, we show for all functions f… Show more

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Cited by 7 publications
(26 citation statements)
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“…Analogous to the reasoning in (1.2), we can use Fubini's theorem to give a sufficient condition on A for which (2.1) is bounded from above. This includes the choice of A studied in [1].…”
Section: Resultsmentioning
confidence: 99%
See 4 more Smart Citations
“…Analogous to the reasoning in (1.2), we can use Fubini's theorem to give a sufficient condition on A for which (2.1) is bounded from above. This includes the choice of A studied in [1].…”
Section: Resultsmentioning
confidence: 99%
“…Thus, we must take into account the size of f . The L 1 norm is a natural choice for measuring the size of a function f : R → R. For our measurement of substructure, we follow Barnard and Steinerberger [1] and investigate, as a function of t,…”
Section: 2mentioning
confidence: 99%
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