Related papers: Multivariate Bounded Variation Functions of Jordan…
We introduce and study multivariate generalizations of the classical BV spaces of Jordan, F. Riesz and Wiener. The family of the introduced spaces contains or is intimately related to a considerable class of function spaces of modern…
We introduce the concept of functions of locally bounded variation on abstract Wiener spaces and study their properties. Some nontrivial examples and applications to stochastic analysis are also discussed.
The first formal development of functions with bounded variation in normed spaces is attributed to Chistyakov [5], and was later extended to the context of 2-normed spaces by Cure, Ferrer S., and Ferrer V. [6]. In this paper, we elaborate…
In this paper, we have investigated the generalized Wiener space of bounded variation with $p$-variable. Various results are obtained such as uniform convexity and reflexivity, there was characterized the set of points of discontinuity of…
We present the foundations of the theory of functions of bounded variation and sets of finite perimeter in abstract Wiener spaces.
The concept of bounded variation has been generalized in many ways. In the frame of functions taking values in Banach space, the concept of bounded semivariation is a very important generalization. The aim of this paper is to provide an…
This paper addresses the study and characterizations of variational convexity of extended-real-valued functions on Banach spaces. This notion has been recently introduced by Rockafellar, and its importance has been already realized and…
Recently the characterization of the compactness in the space $BV([0,1])$ of functions of bounded Jordan variation was given. Here, certain generalizations of this result are given for the spaces of functions of bounded Waterman…
Given a unital algebra $\mathscr A$ of locally Lipschitz functions defined over a metric measure space $({\mathrm X},{\mathsf d},\mathfrak m)$, we study two associated notions of function of bounded variation and their relations: the space…
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…
Let $[a,b]\subset\mathbb{R}$ be a non empty and non singleton closed interval and $P=\{a=x_0<\cdots<x_n=b\}$ is a partition of it. Then $f:I\to\mathbb{R}$ is said to be a function of $r$-bounded variation, if the expression…
We obtain sharp estimates of the Hardy-Vitali type total $p$-variation of a function of two variables in terms of its mixed modulus of continuity in $L^p([0,1]^2)$. We also investigate various embeddings for mixed norm spaces of bivariate…
In the setting of a metric space equipped with a doubling measure and supporting a Poincar\'e inequality, and based on results by Bj\"orn and Shanmugalingam (2007), we show that functions of bounded variation can be extended from any…
Under certain initial conditions, we prove the existence of set-valued selectors of univariate compact-valued multifunctions of bounded (Jordan) variation when the notion of variation is defined taking into account only the Pompeiu…
The recently introduced concept of $\mathcal{D}$-variation unifies previous concepts of variation of multivariate functions. In this paper, we give an affirmative answer to the open question from Pausinger \& Svane (J. Complexity, 2014)…
By the Riesz representation theorem using the Riemann-Stieltjes integral, linear continuous functionals on the set of continuous functions from the unit interval into the reals can either be characterized by functions of bounded variation…
In this paper we show existence of traces of functions of bounded variation on the boundary of a certain class of domains in metric measure spaces equipped with a doubling measure supporting a $1$-Poincar\'e inequality, and obtain $L^1$…
We study the predual of the space of functions of bounded variation defined over a metric measure space $({\rm X},{\sf d},\mathfrak m)$ with $\mathfrak m$ finite. More specifically, for any exponent $p\in(1,\infty)$ we construct an…
We investigate the invariant metrics and complex geodesics in the universal Teichm\"{u}ller space and Teichm\"{u}ller space of the punctured disk using Milin's coefficient inequalities. This technique allows us to establish that all…
In contrast to the univariate case, several definitions are available for the notion of bounded variation for a bivariate function. This article is an attempt to study the Hausdorff dimension and box dimension of the graph of a continuous…