On Hausdorff measure and an inequality due to Maz’ya
Sign Up to like & getrecommendations! Published in 2019 at "Archiv der Mathematik"
DOI: 10.1007/s00013-019-01425-3
Abstract: We give an “elementary” proof of an inequality due to Maz’ya. As a prerequisite we prove an approximation property for the Hausdorff measure. We also comment on the relations between Maz’ya’s inequality, the isoperimetric inequality,… read more here.
Keywords: inequality due; hausdorff measure; measure inequality; due maz ... See more keywords
Hausdorff measure of sets of Dirichlet non-improvable affine forms
Sign Up to like & getrecommendations! Published in 2022 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2022.108353
Abstract: For a non-increasing real valued function $\psi$, a pair $(A,\mathbf{b})$ of a real $m\times n$ matrix $A$ and $\mathbf{b}\in\mathbb{R}^m$ is said to be $\psi$-Dirichlet improvable if the system $$\|A\mathbf{q}+\mathbf{b}-\mathbf{p}\|^m < \psi(T)\quad\text{and}\quad\|\mathbf{q}\|^n < T$$ has a… read more here.
Keywords: dirichlet non; hausdorff measure; non improvable; mathbf ... See more keywords
On a relationship between the Hausdorff measure and the density of the thinnest covering of Rn
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2020.124667
Abstract: Abstract In this paper, we prove a reciprocal relationship between the Hausdorff h-measure and the density of the thinnest covering of R n by translates of the unit ball. More precisely, we will prove μ… read more here.
Keywords: hausdorff measure; thinnest covering; density thinnest; relationship hausdorff ... See more keywords
JARNÍK TYPE THEOREMS ON MANIFOLDS
Sign Up to like & getrecommendations! Published in 2023 at "Bulletin of the Australian Mathematical Society"
DOI: 10.1017/s0004972723000291
Abstract: Let $\psi $ be a decreasing function. We prove zero-infinity Hausdorff measure criteria for the set of dual $\psi $ -approximable points and for the set of inhomogeneous multiplicative $\psi $ -approximable points on nondegenerate… read more here.
Keywords: hausdorff measure; jarn type; type theorems; theorems manifolds ... See more keywords