P. Ivanisvili

activity

20162026

most citedOn the failure of lower square function estimates in the non-homogeneous weighted setting

1 citations · 2 across the 38 of their papers we have counts for

collaborators

Showing 2024Show all

6 papers · 1 filter

math.FA2024

Jackson's inequality on the hypercube

Paata Ivanisvili, Roman Vershynin, Xinyuan Xie

We investigate the best constant $J (n, d)$ such that Jackson's inequality \[ \inf_{\mathrm{deg}(g) \leq d} \|f - g\|_{\infty} \leq J(n,d) \, s(f), \] holds for all functions $f$ on…

math.FA2024

$(P, Q)$ complex hypercontractivity

Paata Ivanisvili, Pavlos Kalantzopoulos

Let $ξ$ be the standard normal random vector in $R^{k}$ . Under some mild growth and smoothness assumptions on any increasing $P, Q : [0, \infty) \mapsto [0, \infty)$ we sh…

math.PR2024

Sharpening the gap between $L^{1}$ and $L^{2}$ norms

Paata Ivanisvili, Yonathan Stone

We refine the classical Cauchy--Schwartz inequality $∥ X ∥_{1} \leq ∥ X ∥_{2}$ by demonstrating that for any $p$ and $q$ with $q > p > 2$ , there exists a constant $C = C (p, q)$ such that…

math.FA2024

On the Eldan-Gross inequality

Paata Ivanisvili, Haonan Zhang

A recent discovery of Eldan and Gross states that there exists a universal $C > 0$ such that for all Boolean functions $f : {- 1, 1}^{n} \to {- 1, 1}$ , $$ \int_{\{-1,1\}^n}\sqrt{s_f(x)}dμ…

math.CA2024

Sharp isoperimetric inequalities on the Hamming cube near the critical exponent

Polona Durcik, Paata Ivanisvili, Joris Roos

An isoperimetric inequality on the Hamming cube for exponents $β \geq 0.50057$ is proved, achieving equality on any subcube. This was previously known for $β\ge \log_2(3/2)\approx 0.…

math.CO2024

Discrete Brunn-Minkowski Inequality for subsets of the cube

Lars Becker, Paata Ivanisvili, Dmitry Krachun +1

We show that for all $A, B \subseteq {0, 1, 2}^{d}$ we have $∣ A + B ∣ \geq (∣ A ∣∣ B ∣)^{l o g (5) / (2 l o g (3))} .$ We also show that for all finite $A, B \subset Z^{d}$ , and any $V…

Jackson's inequality on the hypercube

(P,Q) complex hypercontractivity

Sharpening the gap between L1 and L2 norms

On the Eldan-Gross inequality

Sharp isoperimetric inequalities on the Hamming cube near the critical exponent

Discrete Brunn-Minkowski Inequality for subsets of the cube

$(P, Q)$ complex hypercontractivity

Sharpening the gap between $L^{1}$ and $L^{2}$ norms