A Proof of a Conjecture of Bobkov and Houdré

S. Kwapien, M. Pycia, W. Schachermayer
1996 Electronic Communications in Probability  
S.G. Bobkov and C. Houdré recently posed the following question on the Internet ([1]): Let X, Y be symmetric i.i.d. random variables such that:
doi:10.1214/ecp.v1-972 fatcat:35wb5vil6ngc7koyvp7b3q7qxi