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.
Besicovitch type maximal operators an d applications to Fourier analysis
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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.