A. Tyulenev

activity

20142026

most citedSome new function spaces of variable smoothness

12 citations · 22 across the 11 of their papers we have counts for

collaborators

13 papers

math.FA2026

A New insight into the Ambrosio--Reshetnyak approach to Sobolev maps

Alexander Tyulenev

Given $p \in (1, \infty)$ , let $X = (X, ρ, μ)$ be a metric measure space such that the measure $μ$ is uniformly locally doubling and $X$ sup…

math.CA2026

Catching jumps of metric-valued mappings with Lipschitz functions

Dmitriy Stolyarov, Alexander Tyulenev

It follows from recent results of V. Bakhtin, R. Oleinik, and the second named author that, given a metric space $X$ , a continuous map $γ : [a, b] \to X$ is…

math.FA2024

Characterization of AC and Sobolev curves via Lipschitz post-compositions

Roman D. Oleinik, Alexander I. Tyulenev

Let $X := (X, d)$ be an arbitrary metric space. For each $p \in [1, \infty]$ , we prove that a map $γ : [a, b] \to X$ is $p$ -abs…

math.FA2023

Traces of Sobolev spaces to piecewise Ahlfors--David regular sets

Alexander Tyulenev

Let $(X, d, μ)$ be a metric measure space with uniformly locally doubling measure $μ$ . Given $p \in (1, \infty)$ , assume that $(\operatorname{X},\operato…

math.FA2023

Traces of Sobolev spaces to irregular subsets of metric measure spaces

Alexander Tyulenev

Given $p \in (1, \infty)$ , let $(X, d, μ)$ be a metric measure space with uniformly locally doubling measure $μ$ supporting a weak local $(1, p)$ -Poincaré…

math.FA2021★ 5 cited

Almost sharp descriptions of traces of Sobolev $W_{p}^{1} (R^{n})$ -spaces to arbitrary compact subsets of $R^{n}$ . The case $p \in (1, n]$

Alexander Tyulenev

Let $S \subset R^{n}$ be an arbitrary nonempty compact set such that the $d$ -Hausdorff content $H_{\infty}^{d} (S) > 0$ for some $d \in (0, n]$ . For each $p \in (\…

math.FA2021

Some porosity-type properties of sets related to the $d$ -Hausdorff content

Alexander Tyulenev

Let $S \subset R^{n}$ be a nonempty set. Given $d \in [0, n)$ and a cube $Q \subset R^{n}$ with $l = l (Q) \in (0, 1]$ , we show that if the $d$ -H…

math.FA2020★ 2 cited

Restrictions of Sobolev $W_{p}^{1} (R^{2})$ -spaces to planar rectifiable curves

Alexander Tyulenev

We construct explicit examples of Frostman-type measures concentrated on arbitrary planar rectifiable curves of positive length. Based on such constructions we obtain for each $p \…

math.FA2016

Sobolev $W_{p}^{1} (R^{n})$ spaces on $d$ -thick closed subsets of $R^{n}$

A. I. Tyulenev, S. K. Vodop'yanov

Let $S \subset R^{n}$ be a~closed set such that for some $d \in [0, n]$ and $ε > 0$ the~ $d$ -Hausdorff content $\mathcal{H}^{d}_{\infty}(S \cap Q(x,r)) \geq \varep…

math.FA2016★ 1 cited

Besov-type spaces of variable smoothness on rough domains

A. I. Tyulenev

The paper puts forward new Besov spaces of variable smoothness $B_{p, q}^{φ_{0}} (G, {t_{k}})$ and $B_{p, q, r}^{l} (Ω, {t_{k}})$ on rough domains. A~domain~ $G$ is either…

math.FA2015★ 1 cited

Traces of weighted Sobolev spaces with Muckenhoupt weight. The case $p = 1$

A. I. Tyulenev

A complete description of traces on $R^{n}$ of functions from the weighted Sobolev space $W_{1}^{l} (R^{n + 1}, γ)$ , $l \in N$ , with weight $γ\in A^{\rm loc}…

math.FA2015★ 1 cited

On various approaches to Besov-type spaces of variable smoothness

A. I. Tyulenev

The paper is concerned with Besov spaces of variable smoothness $B_{p, q}^{φ_{0}} (R^{n}, {t_{k}})$ , in which the norms are defined in terms of convolutions with smooth fun…

math.FA2014★ 12 cited

Some new function spaces of variable smoothness

A. I. Tyulenev

The present paper is concerned with new Besov-type space of variable smoothness. Nonlinear spline-approximation approach is used to give atomic decomposition of such space. Charact…

A New insight into the Ambrosio--Reshetnyak approach to Sobolev maps

Catching jumps of metric-valued mappings with Lipschitz functions

Characterization of AC and Sobolev curves via Lipschitz post-compositions

Traces of Sobolev spaces to piecewise Ahlfors--David regular sets

Traces of Sobolev spaces to irregular subsets of metric measure spaces

Almost sharp descriptions of traces of Sobolev Wp1​(Rn)-spaces to arbitrary compact subsets of Rn. The case p∈(1,n]

Some porosity-type properties of sets related to the d-Hausdorff content

Restrictions of Sobolev Wp1​(R2)-spaces to planar rectifiable curves

Sobolev Wp1​(Rn) spaces on d-thick closed subsets of Rn

Besov-type spaces of variable smoothness on rough domains

Traces of weighted Sobolev spaces with Muckenhoupt weight. The case p=1

On various approaches to Besov-type spaces of variable smoothness

Some new function spaces of variable smoothness

Almost sharp descriptions of traces of Sobolev $W_{p}^{1} (R^{n})$ -spaces to arbitrary compact subsets of $R^{n}$ . The case $p \in (1, n]$

Some porosity-type properties of sets related to the $d$ -Hausdorff content

Restrictions of Sobolev $W_{p}^{1} (R^{2})$ -spaces to planar rectifiable curves

Sobolev $W_{p}^{1} (R^{n})$ spaces on $d$ -thick closed subsets of $R^{n}$

Traces of weighted Sobolev spaces with Muckenhoupt weight. The case $p = 1$