Sharp inequality |A1+⋯+An| ≥ (∏|Ai|)^{1/p} holds with p = n log(m+1)/log(nm+1) for Ai ⊆ {0..m}^d, exponent optimal, obtained from a functional inequality on Z^d.
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Sharp Lower Bounds for Sumsets in Hypercubes
Sharp inequality |A1+⋯+An| ≥ (∏|Ai|)^{1/p} holds with p = n log(m+1)/log(nm+1) for Ai ⊆ {0..m}^d, exponent optimal, obtained from a functional inequality on Z^d.