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

18 papers

math.CA2021

Hypercontractivity of the semigroup of the fractional laplacian on the n-sphere

Rupert L. Frank, Paata Ivanisvili

For $1 < p \leq q$ we show that the Poisson semigroup $e^{- t - Δ}$ on the $n$ -sphere is hypercontractive from $L^{p}$ to $L^{q}$ in dimensions $n \leq 3$ if and only if $e^{-t\sq…

math.CA2020

Sharp growth of the Ornstein-Uhlenbeck operator on Gaussian tail spaces

Alexandros Eskenazis, Paata Ivanisvili

Let $X$ be a standard Gaussian random variable. For any $p \in (1, \infty)$ , we prove the existence of a universal constant $C_{p} > 0$ such that the inequality $$(\mathbb{E} |h'(X)|…

math.FA2020

Hyper contractivity on the unit circle for ultraspherical measures: linear case

Paata Ivanisvili, Alexander Lindenberger, Paul F. X. Müller +1

In this paper we extend complex uniform convexity estimates for $C$ to $R^{n}$ and determine best constants. Furthermore we provide the link to log-Sobolev inequal…

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.FA2019

Polynomial inequalities on the Hamming cube