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Sharp isoperimetric inequalities on the Hamming cube II: The critical exponent
Polona Durcik, Paata Ivanisvili, Joris Roos +1
A sharp isoperimetric inequality for the Hamming cube is proved at the critical exponent . This follows up on previous work, where such bounds were established for n…
Optimal Young's convolutions inequality and its reverse form on the hypercube
David Beltran, Paata Ivanisvili, José Madrid +1
We establish sharp forms of Young's convolution inequality and its reverse on the discrete hypercube in the diagonal case . As applications, we derive bounds for a…
Sharp Lower Bounds for Dyadic Square Functions of indicator functions of sets
Natanael Alpay, Paata Ivanisvili
We study lower bounds for dyadic square functions of indicator functions. In the case of the dyadic square function we obtain a sharp lower bound: for every measurable $A \…
Hypercontractivity of the semigroup of the fractional laplacian on the n-sphere
Rupert L. Frank, Paata Ivanisvili
For we show that the Poisson semigroup on the -sphere is hypercontractive from to in dimensions if and only if $e^{-t\sq…
Sharp growth of the Ornstein-Uhlenbeck operator on Gaussian tail spaces
Alexandros Eskenazis, Paata Ivanisvili
Let be a standard Gaussian random variable. For any , we prove the existence of a universal constant such that the inequality $$(\mathbb{E} |h'(X)|…
Dimension independent Bernstein-Markov inequalities in Gauss space
Alexandros Eskenazis, Paata Ivanisvili
We obtain the following dimension independent Bernstein-Markov inequality in Gauss space: for each there exists a constant such that for any and…