相关论文: A Remark on an Integral Characterization of the Du…

This article characterizes conjugates and subdifferentials of convex integral functionals over the linear space $\mathcal N^\infty$ of stochastic processes of essentially bounded variation (BV) when $\mathcal N^\infty$ is identified with…

We present the foundations of the theory of functions of bounded variation and sets of finite perimeter in abstract Wiener spaces.

For a pair of bounded linear Hilbert space operators $A$ and $B$ one considers the Lebesgue type decompositions of $B$ with respect to $A$ into an almost dominated part and a singular part, analogous to the Lebesgue decomposition for a pair…

We derive the bilateral estimates for the module of continuity of the fractional integrals and derivatives for the functions from the classical Lebesgue-Riesz spaces.

In this paper we investigate the relationship between the properties of a compact set $\sigma \subseteq \mathbb{C}$ and the structure of the space $BV(\sigma)$ of functions of bounded variation (in the sense of Ashton and Doust) defined on…

We develop a theory of bounded variation functions and Besov spaces in abstract Dirichlet spaces which unifies several known examples and applies to new situations, including fractals.

We generalize the extension and trace results of Bj\"orn-Bj\"orn-Shanmugalingam \cite{BBS21} to the setting of complete noncompact doubling metric measure spaces and their uniformized hyperbolic fillings. This is done through a…

We characterize the positive radial continuous and rotation invariant valuations $V$ defined on the star bodies of $\mathbb R^n$ as the applications on star bodies which admit an integral representation with respect to the Lebesgue measure.…

We extend the classical Lebesgue and Fubini differentiation theorems to functions of several variables, using the notions of joint derivative and joint monotonicity. Our first main result shows that for a function $f$ of bounded variation,…

Two representations theorems are presented: 1. Any Borel action of a second countable locally compact group $G$ on a standard Borel space $X$ admits an injective $G$-equivariant Borel map into the shift space of $1$-Lipschitz functions from…

It is well-known that a random variable, i.e., a function defined on a probability space, with values in a Borel space, can be represented on the special probability space consisting of the unit interval with Lebesgue measure. We show an…

We give an extension of the theory of relaxation of variational integrals in classical Sobolev spaces to the setting of metric Sobolev spaces. More precisely, we establish a general framework to deal with the problem of finding an integral…

In this paper, we study properties of the bilinear multiplier space. We give a necessary condition for a continuous integrable function to be a bilinear multiplier on variable exponent Lebesgue spaces. And we prove the localization theorem…

In metric measure spaces, we study boundary traces of BV functions in domains equipped with a doubling measure and supporting a Poincar\'e inequality, but possibly having a very large and irregular boundary. We show that the trace exists in…

We prove various results in infinite-dimensional differential calculus which relate differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: 1. in the…

Given a monotone convex function on the space of essentially bounded random variables with the Lebesgue property (order continuity), we consider its extension preserving the Lebesgue property to as big solid vector space of random variables…

The bounded variation seminorm and the Sobolev seminorm on compact manifolds are represented as a limit of fractional Sobolev seminorms. This establishes a characterization of functions of bounded variation and of Sobolev functions on…

Let $\precsim$ be a reflexive binary relation on a topological space $(X, \tau )$. A pair $(u,v)$ of continuous real-valued functions on $(X, \tau )$ is said to be a {\em continuous representation} of $\precsim$ if, for all $x,y \in X$,…

In this paper, the central BMO spaces with variable exponent are introduced. As an application, we characterize these spaces by the boundedness of commutators of Hardy operator and its dual operator on variable Lebesgue spaces. The…

We introduce first weighted function spaces on Rd using the Dunkl convolution that we call Besov-Dunkl spaces. We provide characterizations of these spaces by decomposition of functions. Next we obtain in the real line and in radial case on…