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pro vyhledávání: '"30l99"'
Autor:
Dias, Manuel, Tewodrose, David
The symmetrized Asymptotic Mean Value Laplacian $\tilde{\Delta}$, obtained as limit of approximating operators $\tilde{\Delta}_r$, is an extension of the classical Euclidean Laplace operator to the realm of metric measure spaces. We show that, as $r
Externí odkaz:
http://arxiv.org/abs/2411.10202
Autor:
Hoffman, John
We provide new characterizations of the $BMO$-Sobolev space $I_{\alpha}(BMO)$ for the range $0 < \alpha <2$. When $0 < \alpha <1$, our characterizations are in terms of square functions measuring multiscale approximation of constants, and when $1 \le
Externí odkaz:
http://arxiv.org/abs/2410.11724
Autor:
Lê, Trí Minh, Tapia-García, Sebastián
Eikonal equations in metric spaces have strong connections with the local slope operator (or the De Giorgi slope). In this manuscript, we explore and delve into an analogous model based on the global slope operator, expressed as $\lambda u + G[u] = \
Externí odkaz:
http://arxiv.org/abs/2410.00530
Autor:
Caputo, Emanuele, Cavallucci, Nicola
We define the chain Sobolev space on a possibly non-complete metric measure space in terms of chain upper gradients. In this context, $\varepsilon$-chains are a finite collection of points with distance at most $\varepsilon$ between consecutive point
Externí odkaz:
http://arxiv.org/abs/2408.15071
We study the fundamental properties of pointwise semi-Lipschitz functions between asymmetric spaces, which are the natural asymmetric counterpart of pointwise Lipschitz functions. We also study the influence that partial symmetries of a given space m
Externí odkaz:
http://arxiv.org/abs/2407.17574
Autor:
Shalukhina, Alina
We prove the self-improvement property of the Hardy--Littlewood maximal operator on quasi-Banach lattices with the Fatou property in the setting of spaces of homogeneous type. Our result is a generalization of the boundedness criterion obtained in 20
Externí odkaz:
http://arxiv.org/abs/2406.03382
Autor:
Zimmerman, Scott
This paper gives an alternate, elementary proof of a result of Magnani: maps between Carnot groups that preserve horizontal curves and are continuously differential in horizontal directions in the Euclidean sense are continuously Pansu differentiable
Externí odkaz:
http://arxiv.org/abs/2405.12138
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
Autor:
Allu, Vasudevarao, Pandey, Abhishek
In this paper, we introduce the concept of quasihyperbolically visible spaces. As a tool, we study the connection between the Gromov boundary and the metric boundary.
Comment: 12 pages. Comments are welcome. arXiv admin note: text overlap with a
Comment: 12 pages. Comments are welcome. arXiv admin note: text overlap with a
Externí odkaz:
http://arxiv.org/abs/2405.10273
Autor:
Alam, Aftab
In this paper, we introduce the notions of proximally completeness, proximally closedness and proximally continuity and utilize the same to prove a result on existence and uniqueness of best proximity points in the setting of metric space (not necess
Externí odkaz:
http://arxiv.org/abs/2405.02635