D. Stolyarov

activity

20092023

most citedAnisotropic Ornstein non inequalities

12 citations · 41 across the 31 of their papers we have counts for

collaborators

41 papers

math.CA2023★ 1 cited

Martingale transforms of bounded random variables and indicator functions of events

Dmitriy Stolyarov, Vasily Vasyunin, Pavel Zatitskii

We provide sharp estimates for the distribution function of a martingale transform of the indicator function of an event. They are formulated in terms of Burkholder functions, whic…

math.FA2023

Alberti's type rank one theorem for martingales

Rami Ayoush, Dmitriy Stolyarov, Michał Wojciechowski

We prove that the polar decomposition of the singular part of a vector measure depends on its conditional expectations computed with respect to the $q$ -regular filtration. This dep…

math.CA2023

Bellman functions on simple non-convex domains in the plane

Paata Ivanisvili, Dmitriy Stolyarov, Vasily Vasyunin +1

The present paper provides a generalization of the previous authors' work on Bellman functions for integral functionals on $BMO$ . Those Bellman functions are the minimal l…

math.CA2023

On embedding of Besov spaces of zero smoothness into Lorentz spaces

Dmitriy Stolyarov

We show that the zero smoothness Besov space $B_{p, q}^{0, 1}$ does not embed into the Lorentz space $L_{p, q}$ unless $p = q$ ; here $p, q \in (1, \infty)$ . This answers negatively a quest…

math.PR2022

Trace inequalities for Sobolev martingales

Dmitriy Stolyarov

We study limiting trace inequalities in the style of Maz'ya and Meyers--Ziemer for Sobolev martingales. We develop the Bellman function approach to such estimates, which allows to…

math.CA2022

On locally concave functions on simplest non-convex domains

Dmitriy Stolyarov, Pavel Zatitskiy

We prove that certain Bellman functions of several variables are the minimal locally concave functions. This generalizes earlier results about Bellman functions of two variables.

math.CA2022

On Fourier multipliers with rapidly oscillating symbols

Dmitriy Stolyarov

We provide asymptotically sharp bounds for the $L_{p}$ norms of the Fourier multipliers with the symbols $e^{iλ φ (ξ /∣ ξ ∣)}$ , where $λ \in R$ is a large parameter.

math.MG2022

Inner and outer smooth approximation of convex hypersurfaces. When is it possible?

Daniel Azagra, Dmitriy Stolyarov

Let $S$ be a convex hypersurface (the boundary of a closed convex set $V$ with nonempty interior) in $R^{n}$ . We prove that $S$ contains no lines if and only if for every op…

math.CA2021

Fractional integration of summable functions: Maz'ya's $Φ$ -inequalities

Dmitriy Stolyarov

We study the inequalities of the type $∣ \int_{R^{d}} Φ (K * f) ∣ ≲ ∥ f ∥_{L_{1} (R^{d})}^{p}$ , where the kernel $K$ is homogeneous of order $α - d$ and possibly vector-v…

math.FA2021★ 8 cited

A trace inequality for solenoidal charges

Bogdan Raita, Daniel Spector, Dmitriy Stolyarov

We prove that for $α \in (d - 1, d]$ , one has the trace inequality \begin{align*} \int_{\mathbb{R}^d} |I_αF| \;dν\leq C |F|(\mathbb{R}^d)\|ν\|_{\mathcal{M}^{d-α}(\mathbb{R}^d)} \end{al…

math.CA2021★ 1 cited

On $Φ$ -inequalities for martingale fractional integration and their Bellman functions

Dmitriy Stolyarov

Inspired by a conjecture of Vladimir Maz'ya on $Φ$ -inequalities in the spirit of Bourgain and Brezis, we establish some $Φ$ -inequalities for fractional martingale transforms. These…

math.PR2021★ 4 cited

Sharp moment estimates for martingales with uniformly bounded square functions

Dmitriy Stolyarov, Vasily Vasyunin, Pavel Zatitskiy +1

We provide sharp bounds for the exponential moments and $p$ -moments, $1 ⩽ p ⩽ 2$ , of the terminate distribution of a martingale whose square function is uniformly bo…

math.CA2020

Dimension estimates for vectorial measures with restricted spectrum

Dmitriy Stolyarov

We link the problem of estimating the lower Hausdorff dimension of PDE or Fourier constrained measures with Harnack's inequalities for the heat equation. Our approach provides new…

math.CA2020

Hardy--Littlewood--Sobolev inequality for $p = 1$

Dmitriy Stolyarov

Let $W$ be a closed dilation and translation invariant subspace of the space of $R^{ℓ}$ -valued Schwartz distributions in $d$ variables. We show that if the spac…

math.PR2020

Fractional integration for irregular martingales

Dmitriy Stolyarov, Dmitry Yarcev

We suggest two versions of the Hardy--Littlewood--Sobolev inequality for discrete time martingales. In one version, the fractional integration operator is a martingale transform, h…

math.CA2020

Weakly canceling operators and singular integrals

Dmitriy Stolyarov

We suggest an elementary Harmonic Analysis approach to canceling and weakly canceling differential operators, which allows to extend these notions to anisotropic setting and also r…

math.CA2020

Hausdorff dimension of measures with arithmetically restricted spectrum

Rami Ayoush, Dmitriy Stolyarov, Michał Wojciechowski

We provide an estimate from below for the lower Hausdorff dimension of measures on the unit circle based on the arithmetic properties of their spectra. We obtain our bounds via app…

math.CA2020

Sharp mutliplicative inequalities with $BMO$ $I$

Dmitriy Stolyarov, Vasily Vasyunin, Pavel Zatitskiy

We find the best possible constant $C$ in the inequality $∥ φ ∥_{L^{r}} \leq C ∥ φ ∥_{L^{p}}^{\frac{p}{r}} ∥ φ ∥_{BMO}^{1 - \frac{p}{r}}$ , where $2 \leq r$ and $p < r$ . We employ t…

math.CA2019

Martingale interpretation of weakly cancelling differential operators

Dmitriy Stolyarov

We provide martingale analogs of weakly cancelling differential operators and prove a Sobolev-type embedding theorem for these operators in the martingale setting.

math.CA2019★ 1 cited

Sharp transference principle for $BMO$ and $A_{p}$

Dmitriy Stolyarov, Pavel Zatitskiy

We provide a version of the transference principle. It says that certain optimization problems for functions on the circle, the interval, and the line have the same answers. In par…

math.CA2018★ 2 cited

Martingale approach to Sobolev embedding theorems

Rami Ayoush, Dmitriy Stolyarov, Michal Wojciechowski

We prove a martingale analog of van Schaftingen's theorem and give sharp estimates on the lower Hausdorff dimension of measures in martingale shift invariant spaces. We also provid…

math.CA2018

Restrictions of higher derivatives of the Fourier transform

Michael Goldberg, Dmitriy Stolyarov

We consider several problems related to the restriction of $(\nabla^{k}) f^$ to a surface $Σ \subset R^{d}$ with nonvanishing Gauss curvature. While such restrictions clear…

math.CA2017

Sharpening Hölder's inequality

Haakan Hedenmalm, Dmitriy M. Stolyarov, Vasily I. Vasyunin +1

We strengthen Hölder's inequality. The new family of sharp inequalities we obtain might be thought of as an analog of Pythagorean theorem for the $L^{p}$ spaces. Our reasonings rely…

math.CV2016★ 1 cited

Uniform approximation of Bloch functions and the boundedness of the integration operator on $H^{\infty}$

Wayne Smith, Dmitriy M. Stolyarov, Alexander Volberg

We obtain a necessary and sufficient condition for the operator of integration to be bounded on $H^{\infty}$ in a simply connected domain. The main ingredient of the proof is a new r…

Martingale transforms of bounded random variables and indicator functions of events

Alberti's type rank one theorem for martingales

Bellman functions on simple non-convex domains in the plane

On embedding of Besov spaces of zero smoothness into Lorentz spaces

Trace inequalities for Sobolev martingales

On locally concave functions on simplest non-convex domains

On Fourier multipliers with rapidly oscillating symbols

Inner and outer smooth approximation of convex hypersurfaces. When is it possible?

Fractional integration of summable functions: Maz'ya's Φ-inequalities

A trace inequality for solenoidal charges

On Φ-inequalities for martingale fractional integration and their Bellman functions

Sharp moment estimates for martingales with uniformly bounded square functions

Dimension estimates for vectorial measures with restricted spectrum

Hardy--Littlewood--Sobolev inequality for p=1

Fractional integration for irregular martingales

Weakly canceling operators and singular integrals

Hausdorff dimension of measures with arithmetically restricted spectrum

Sharp mutliplicative inequalities with BMO I

Martingale interpretation of weakly cancelling differential operators

Sharp transference principle for BMO and Ap​

Martingale approach to Sobolev embedding theorems

Restrictions of higher derivatives of the Fourier transform

Sharpening Hölder's inequality

Uniform approximation of Bloch functions and the boundedness of the integration operator on H∞

Fractional integration of summable functions: Maz'ya's $Φ$ -inequalities

On $Φ$ -inequalities for martingale fractional integration and their Bellman functions

Hardy--Littlewood--Sobolev inequality for $p = 1$

Sharp mutliplicative inequalities with $BMO$ $I$

Sharp transference principle for $BMO$ and $A_{p}$

Uniform approximation of Bloch functions and the boundedness of the integration operator on $H^{\infty}$