Hypercontractivity of Spherical Averages in Hamming Space
نویسندگان
چکیده
منابع مشابه
Hypercontractivity of spherical averages in Hamming space
Consider a linear space of functions on the binary hypercube and a linear operator Tδ acting by averaging a function over a Hamming sphere of radius δn. It is shown that such an operator has a dimension independent bound on the norm Lp → L2 with p = 1 + (1 − 2δ). This result evidently parallels a classical estimate of Bonami and Gross for Lp → Lq norms for the operator of convolution with a Ber...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2019
ISSN: 0895-4801,1095-7146
DOI: 10.1137/15m1046575