Hypercontractivity of Spherical Averages in Hamming Space

SIAM JOURNAL ON DISCRETE MATHEMATICS, pp. 731-754, 2019.

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Abstract:

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

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