Abstract
We discuss an elementary trick that sometimes yields simple proofs of integral inequalities of the kind ∫ χ (f s − g s) dμ ⩾ 0. We use this trick to obtain “computation-free” proofs of two famous theorems: Ball’s theorem on the sections of a cube and Haagerup’s theorem on the sharp constants in the Khinchin inequality for Rademacher functions.
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References
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Nazarov, F.L., Podkorytov, A.N. (2000). Ball, Haagerup, and Distribution Functions. In: Havin, V.P., Nikolski, N.K. (eds) Complex Analysis, Operators, and Related Topics. Operator Theory: Advances and Applications, vol 113. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8378-8_21
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DOI: https://doi.org/10.1007/978-3-0348-8378-8_21
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9541-5
Online ISBN: 978-3-0348-8378-8
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