Bourgain-Brezis-Mironescu formula for -spaces in arbitrary domains

K Mohanta - Calculus of Variations and Partial Differential …, 2024 - Springer
Under certain restrictions on s, p, q, the Triebel-Lizorkin spaces can be viewed as
generalised fractional Sobolev spaces W qs, p. In this article, we show that the Bourgain …

[HTML][HTML] Functional and variational aspects of nonlocal operators associated with linear PDEs

A Arroyo-Rabasa - Nonlinear Analysis, 2025 - Elsevier
We introduce a general difference quotient representation for non-local operators
associated with a first-order linear operator. We establish new local to non-local estimates …

Maz'ya–Shaposhnikova meet Bishop–Gromov

BX Han, A Pinamonti, Z Xu, K Zambanini - Potential Analysis, 2024 - Springer
We find a surprising link between Maz'ya–Shaposhnikova's well-known asymptotic formula
concerning fractional Sobolev seminorms and the generalized Bishop–Gromov inequality. In …

Bougain-Brezis-Mironescu formula for Triebel-Lizorkin spaces in arbitrary domains

K Mohanta - arxiv preprint arxiv:2308.12830, 2023 - arxiv.org
We show that the Bourgain-Brezis-Mironescu formula, regarding the limits of Gagliardo-type
seminorms as $ s\to 1-$, holds for Triebel-Lizorkin spaces defined in arbitrary domains. This …

A metric counterpart of the Gu-Yung formula

S Buccheri, W Górny - arxiv preprint arxiv:2403.13475, 2024 - arxiv.org
In this note we consider a generalisation to the metric setting of the recent work [Gu-Yung,
JFA 281 (2021), 109075]. In particular, we show that under relatively weak conditions on a …