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Bourgain discretization using Lebesgue-Bochner spaces

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Abstract We study the Lebesgue-Bochner discretization property of Banach spaces Y , which ensures that the Bourgain discretization modulus for Y has a good lower estimate. We prove that there… Click to show full abstract

Abstract We study the Lebesgue-Bochner discretization property of Banach spaces Y , which ensures that the Bourgain discretization modulus for Y has a good lower estimate. We prove that there exist spaces that do not have the Lebesgue-Bochner discretization property, and we give a class of examples of spaces that enjoy this property.

Keywords: discretization; discretization using; bourgain discretization; using lebesgue; lebesgue bochner

Journal Title: Quaestiones Mathematicae
Year Published: 2019

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