The homogeneous and original arithmetic Kakeya inequalities are equivalent, leading to new upper bounds for the d-dimensional arithmetic Kakeya constant and new Minkowski dimension lower bounds for (n,d)-Besicovitch sets.
Bourgain, λ p-sets in analysis: results, problems and related aspects, i n: Handbook of the geometry of Banach spaces, Vol
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Generalized Arithmetic Kakeya
The homogeneous and original arithmetic Kakeya inequalities are equivalent, leading to new upper bounds for the d-dimensional arithmetic Kakeya constant and new Minkowski dimension lower bounds for (n,d)-Besicovitch sets.