P. Ivanisvili

activity

20162026

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

1 citations · 2 across the 32 of their papers we have counts for

collaborators

Showing 2017 · math.APShow all

6 papers · 2 filters

math.AP2017

Bobkov's inequality via optimal control theory

Franck Barthe, Paata Ivanisvili

We give the simple proof of Bobkov's inequality using the arguments of dynamical programming principle. As a byproduct of the method we obtain a characterization of optimizers.

math.AP2017

Superexponential estimates and weighted lower bounds for the square function

Paata Ivanisvili, Sergei Treil

We prove the following superexponential distribution inequality: for any integrable $g$ on $[0, 1)^{d}$ with zero average, and any $λ > 0$ \[ |\{ x \in [0,1)^{d} \; :\; g \geqλ\}| \le…

math.AP2017

From discrete flow of Beckner to continuous flow of Janson in complex hypercontractivity

Paata Ivanisvili, Alexander Volberg

We show how Beckner's montonicity result on Hamming cube easily implies the monotonicity of a flow introduced by Janson in Hausdorff--Young inequality

math.AP2017

Convolution estimates and the number of disjoint partitions

Paata Ivanisvili

Let $X$ be a finite collection of sets. We count the number of ways a disjoint union of $n - 1$ subsets in $X$ is a set in $X$ , and estimate this number from above by $∣ X ∣^{c (n)}$ wh…

math.AP2017

Square functions and the Hamming cube: Duality

Paata Ivanisvili, Fedor Nazarov, Alexander Volberg

For $1 < p \leq 2$ , any $n \geq 1$ and any $f : {- 1, 1}^{n} \to R$ , we obtain $(E ∣\nabla f ∣^{p})^{1/ p} \geq C (p) (E ∣ f ∣^{p} - ∣ E f ∣^{p})^{1/ p}$ where $…

math.AP2017★ 1 cited

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

K. Domelevo, P. Ivanisvili, S. Petermichl +2

We show that the classical $A_{\infty}$ condition is not sufficient for a lower square function estimate in the non-homogeneous weighted $L^{2}$ space. We also show that under the ma…