Poincaré inequality 3/2 on the Hamming cube

• Paata Ivanisvili ^[2] ; Alexander Volberg ^[1]
  1. [1] Michigan State University

     Michigan State University

     City of East Lansing, Estados Unidos

     
  2. [2] University of California, Irvine
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 36, Nº 1, 2020, págs. 79-97
• Idioma: inglés
• DOI: 10.4171/rmi/1122
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• Resumen

  • 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.