Between Sobolev and Poincar\'e
  We establish a family of functional inequalities interpolating between the classical logarithmic Sobolev and Poincar\'e inequalities. We prove that they imply the concentration of measure phenomenon intermediate between Gaussian and exponential. Our bounds are close to optimal. 
Rafa{\l} Lata{\l}a (Warsaw University), Krzysztof Oleszkiewicz (Warsaw   University)