Resumen de Poincaré inequality 3/2 on the Hamming cube

Paata Ivanisvili, Alexander Volberg

• For any n≥1, and any f:{−1,1}n→R, we have RE(f+i|∇f|)3/2≤R(Ef)3/2, where z3/2 for z=x+iy is taken with principal branch, and R denotes the real part. We show an application of this inequality: it sharpens a well-known inequality of Beckner.