P. Ivanisvili

activity

20162021

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

1 citations · 1 across the 7 of their papers we have counts for

collaborators

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9 papers · 1 filter

math.AP2019

On Weissler's conjecture on the Hamming cube I

Paata Ivanisvili, Fedor Nazarov

Let $1 \leq p \leq q < \infty$ , and let $w \in C$ . Weissler conjectured that the Hermite operator $e^{w Δ}$ is bounded as an operator from $L^{p}$ to $L^{q}$ on the Hamming c…

math.AP2019

Sharpening the triangle inequality: envelopes between $L^{2}$ and $L^{p}$ spaces

Paata Ivanisvili, Connor Mooney

Motivated by the inequality $∥ f + g ∥_{2}^{2} \leq ∥ f ∥_{2}^{2} + 2∥ f g ∥_{1} + ∥ g ∥_{2}^{2}$ , Carbery (2006) raised the question what is the "right" analogue of this estimate in $L^{…

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…

On Weissler's conjecture on the Hamming cube I

Sharpening the triangle inequality: envelopes between L2 and Lp spaces

Bobkov's inequality via optimal control theory

Superexponential estimates and weighted lower bounds for the square function

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

Convolution estimates and the number of disjoint partitions

Sharpening the triangle inequality: envelopes between $L^{2}$ and $L^{p}$ spaces