Dmitriy Stolyarov

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20242026

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4 papers · 1 filter

math.CA2026

Anisotropic Bourgain--Brezis inequalities

Dmitriy Stolyarov

We provide an adjustment of the Hardy--Littlewood--Sobolev inequality for p=1 to the anisotropic setting. Several examples of anisotropic Bourgain--Brezis inequalities are obtained…

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.CA2024

Maz'ya's $Φ$ -inequalities on domains

Dmitriy Stolyarov

We find necessary and sufficient conditions on the function $Φ$ for the inequality $\int_{Ω} Φ (K * f) ≲ ∥ f ∥_{L_{1} (R^{d})}^{p}$ to be true. Here $K$ is a positive…

math.CA2024

New Bellman induction and a weak version of $BMO$

Egor Dobronravov, Dmitriy Stolyarov, Pavel Zatitskii

We enlarge the area of applicability of the Bellman function method to estimates in the spirit of the John--Nirenberg inequality abandoning certain convexity assumptions. As an app…

Anisotropic Bourgain--Brezis inequalities

Catching jumps of metric-valued mappings with Lipschitz functions

Maz'ya's Φ-inequalities on domains

New Bellman induction and a weak version of BMO

Maz'ya's $Φ$ -inequalities on domains

New Bellman induction and a weak version of $BMO$