Hypercontractivity of Spherical Averages in Hamming Space

Consider the linear space of functions on the binary hypercube and the linear operator S-delta acting by averaging a function over a Hamming sphere of radius delta n around every point. It is shown that this operator has a dimension-independent bound on the norm L-p -> L-2 with p = 1+( 1 - 2 delta)(2). This result evidently parallels a cl...More