Geodesic
Square functions and the Hamming cube: Duality
Discrete analysis (2018) Cet article a éte moissonné depuis la source Scholastica

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For $1$, any $n\geq 1$ and any $f:\{-1,1\}^{n} \to \mathbb{R}$, we obtain $(\mathbb{E} |\nabla f|^{p})^{1/p} \geq C(p)(\mathbb{E}|f|^{p} - |\mathbb{E}f|^{p})^{1/p}$ where $C(p)$ is the smallest positive zero of the confluent hypergeometric function ${}_{1}F_{1}(\frac{p}{2(1-p)}, \frac{1}{2}, \frac{x^{2}}{2})$. Our approach is based on a certain duality between the classical square function estimates on the Euclidean space and the gradient estimates on the Hamming cube.
Publié le : 
@article{DAS_2018_a17,
     author = {Paata Ivanisvili and Fedor Nazarov and Alexander Volberg},
     title = {Square functions and the {Hamming} cube: {Duality}},
     journal = {Discrete analysis},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2018_a17/}
}
TY  - JOUR
AU  - Paata Ivanisvili
AU  - Fedor Nazarov
AU  - Alexander Volberg
TI  - Square functions and the Hamming cube: Duality
JO  - Discrete analysis
PY  - 2018
UR  - http://geodesic.mathdoc.fr/item/DAS_2018_a17/
LA  - en
ID  - DAS_2018_a17
ER  - 
%0 Journal Article
%A Paata Ivanisvili
%A Fedor Nazarov
%A Alexander Volberg
%T Square functions and the Hamming cube: Duality
%J Discrete analysis
%D 2018
%U http://geodesic.mathdoc.fr/item/DAS_2018_a17/
%G en
%F DAS_2018_a17
Paata Ivanisvili; Fedor Nazarov; Alexander Volberg. Square functions and the Hamming cube: Duality. Discrete analysis (2018). http://geodesic.mathdoc.fr/item/DAS_2018_a17/