Zobrazeno 1 - 10
of 182
pro vyhledávání: '"Górka, Przemysław"'
In this article, we characterize both Lusin's theorem and the existence of Borel representatives via the regularity properties of the measure in general topological measure spaces. As a corollary, we prove that Borel regularity of the measure is both
Externí odkaz:
http://arxiv.org/abs/2410.21434
Autor:
Górka, Przemysław, Kurowski, Kacper
We provide new characterizations of Sobolev spaces that are true under some mild conditions. We study modified first order Sobolev spaces on metric measure spaces: $\mathrm{TC}$-Newtonian space, $\hat{\mathrm{TC}}$-Newtonian space, and Gigli-like spa
Externí odkaz:
http://arxiv.org/abs/2407.13051
We establish necessary and sufficient conditions guaranteeing compactness of embeddings of fractional Sobolev spaces, Besov spaces, and Triebel-Lizorkin spaces, in the general context of quasi-metric-measure spaces. Although stated in the setting of
Externí odkaz:
http://arxiv.org/abs/2406.18527
Autor:
Dybowski, Michał, Górka, Przemysław
We provide the following result and its discrete equivalent: Let $f \colon I^n \to \mathbb{R}^{n-1}$ be a continuous function. Then, there exist a point $p \in \mathbb{R}^{n-1}$ and a compact subset $S \subset f^{-1}\left[\left\{p\right\}\right]$ whi
Externí odkaz:
http://arxiv.org/abs/2406.13774
We show that the statement ``In every separable pseudometric space there is a maximal non-strictly \delta-separated set.'' implies the axiom of choice for countable families of sets. This gives answers to a question of Dybowski and G\'{o}rka in [M. D
Externí odkaz:
http://arxiv.org/abs/2405.10466
We study the maximal operator on the variable exponent H\"older spaces in the setting of metric measure spaces. The boundedness is proven for metric measure spaces satisfying an annular decay property. Let us stress that there are no assumptions on t
Externí odkaz:
http://arxiv.org/abs/2303.16713
We study the Hardy-Littlewood maximal operator in the Musielak-Orlicz-Sobolev space $W^{1,\varphi}(\mathbb{R}^n)$. Under some natural assumptions on $\varphi$ we show that the maximal function is bounded and continuous in $W^{1,\varphi}(\mathbb{R}^n)
Externí odkaz:
http://arxiv.org/abs/2303.16587
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 October 2024 538(1)
It has been known since 1996 that a lower bound for the measure, $\mu(B(x,r))\geq br^s$, implies Sobolev embedding theorems for Sobolev spaces $M^{1,p}$ defined on metric-measure spaces. We prove that, in fact Sobolev embeddings for $M^{1,p}$ spaces
Externí odkaz:
http://arxiv.org/abs/1903.05793
Autor:
Dymek, Michał1 (AUTHOR), Górka, Przemysław1 (AUTHOR) przemyslaw.gorka@pw.edu.pl
Publikováno v:
Mathematische Nachrichten. Sep2023, Vol. 296 Issue 9, p4317-4334. 18p.