相关论文: BMO-type norms related to the perimeter of sets

We explore the asymptotic behavior of families of Bourgain-Brezis-Mironescu type nonlocal functionals for mappings from metric measure spaces to arbitrary metric spaces. As the first outcome, we obtain a characterization of Sobolev maps and…

A recent paper of Jerison and Figalli proved a relationship between the $H^{1/2}$ norms of smoothed out indicator functions of sets and their perimeter. We continue this line of investigation and extend it in two ways. First, we describe a…

This paper studies functions of bounded mean oscillation (BMO) on metric spaces equipped with a doubling measure. The main result gives characterizations for mappings that preserve BMO. This extends the corresponding Euclidean results by…

In the setting of a metric space equipped with a doubling measure that supports a Poincar\'e inequality, we show that any set of finite perimeter can be approximated in the BV norm by a set whose topological and measure theoretic boundaries…

In this article we study the family of $BMO^p$ spaces, $p \geq 1$, in the general context of metric measure spaces. We give a characterization theorem that allows to describe all possible relations between these spaces considered as sets of…

We consider a very general definition of BMO on a domain in $\mathbb{R}^n$, where the mean oscillation is taken with respect to a basis of shapes, i.e. a collection of open sets covering the domain. We examine the basic properties and…

We prove that a proper holomorphic local isometry between bounded domains with respect to the Bergman metrics is necessarily a biholomorphism. The proof relies on a new method grounded in Information Geometry theories.

In this work, we derive some novel properties of the bimodal normal distribution. Some of its mathematical properties are examined. We provide a formal proof for the bimodality and assess identifiability. We then discuss the maximum…

We study a measure-theoretic notion of connectedness for sets of finite perimeter in the setting of doubling metric measure spaces supporting a weak $(1,1)$-Poincar\'{e} inequality. The two main results we obtain are a decomposition theorem…

We give a notion of BV function on an oriented manifold where a volume form and a family of lower semicontinuous quadratic forms $G_p: T_pM \to [0,\infty]$ are given. When we consider sub-Riemannian manifolds, our definition coincide with…

In a previous paper the authors developed a H^1-BMO theory for unbounded metric measure spaces $(M,\rho,m)$ of infinite measure that are locally doubling and satisfy two geometric properties, called "approximate midpoint" property and…

This work explores new deep connections between John-Nirenberg type inequalities and Muckenhoupt weight invariance for a large class of $BMO$-type spaces. The results are formulated in a very general framework in which $BMO$ spaces are…

The bivariate normal density with unit variance and correlation $\rho$ is well-known. We show that by integrating out $\rho$, the result is a function of the maximum norm. The Bayesian interpretation of this result is that if we put a…

In this paper, we study functions of bounded variation on a complete and connected metric space with finite one-dimensional Hausdorff measure. The definition of BV functions on a compact interval based on pointwise variation is extended to…

We introduce an elementary argument to bound the $\textrm{BMO}$ seminorm of Fourier series with gaps giving in particular a sufficient condition for them to be in this space. Using finer techniques we carry out a detailed study of the…

In this paper, we introduce the BMT distribution as an unimodal alternative to continuous univariate distributions supported on a bounded interval. The ideas behind the mathematical formulation of this new distribution come from computer…

A group is said to be bounded if it has a finite diameter with respect to any bi-invariant metric. In the present paper we discuss boundedness of various groups of diffeomorphisms.

We extend the construction of Garsia-Rodemich spaces in different directions. We show that the new space \textbf{B,} introduced by Bourgain-Brezis-Mironescu \cite{bbm}, can be described via a suitable scaling of the Garsia-Rodemich norms.…

We explore a definition of uniformity on noncompact manifolds that does not require a Riemannian metric, but is equivalent to bounded gemetry. These are unfinished research notes (and will likely never be published), but since they were…

The purpose of this paper is to analyze the asymptotic behaviour in the spirit of $\Gamma$-convergence of BMO-type functionals related to the total variation of a function $u$. Moreover, we deal with a minimization problem coming from…