Dimension growth for iterated sumsets
Abstract
We study dimensions of sumsets and iterated sumsets and provide natural conditions which guarantee that a set F ⊂eq R satisfies B F+F > B F or even H n F 1. Our results apply to, for example, all uniformly perfect sets, which include Ahlfors-David regular sets. Our proofs rely on Hochman's inverse theorem for entropy and the Assouad and lower dimensions play a critical role. We give several applications of our results including an Erdos-Volkmann type theorem for semigroups and new lower bounds for the box dimensions of distance sets for sets with small dimension.
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