A simple proof that the power $\frac{2m}{m+1}$ in the Bohnenblust--Hille inequalities is sharp

Abstract

The power $\frac{2m}{m+1}$ in the polynomial (and multilinear) Bohnenblust--Hille inequality is optimal. This result is well-known but its proof highly nontrivial. In this note we present a quite simple proof of this fact.

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