Bourgain discretization using Lebesgue-Bochner spaces
Abstract
We study the Lebesgue-Bochner discretization property of Banach spaces Y, which ensures that the Bourgain's 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.
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