Related papers: On Banach Structure of Multivariate BV Spaces I

In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we show that functions of bounded variation (BV functions) can be approximated in the strict sense and pointwise uniformly by special…

In this paper we summarize and give examples of a generalization of the coorbit space theory initiated in the 1980's by H.G. Feichtinger and K.H. Gr\"ochenig. Coorbit theory has been a powerful tool in characterizing Banach spaces of…

The spaces $BV(\sigma)$ and $AC(\sigma)$ were introduced as part of a program to find a general theory which covers both well-bounded operators and trigonometrically well-bounded operators acting on a Banach space. Since their initial…

Let $\G$ be any cocompact, discrete subgroup of $\pslr$. In this paper we find estimates for the predual and the uniform Banach space norms in the von Neumann algebras associated with the Berezin' s quantization of a compact Riemann surface…

Given a category of objects, it is both useful and important to know if all the objects in the category may be realised as sub-objects -- via morphisms in the given category -- of a single object in that category enjoying some nice…

Our aim of this paper is to study a family of functional equation in vector and Banach spaces with difference operators, where this family of functional equation is a general mixed additive-quadratic-cubic-quartic functional equations. We…

Let $A$ be a dual Banach algebra with predual $A_\ast$ and consider the following assertions: (A) $A$ is Connes-amenable; (B) $A$ has a normal, virtual diagonal; (C) $A_\ast$ is an injective $A$-bimodule. For general $A$, all that is known…

An extension of the notion of classical equivalence of equivalence in the Batalin--(Fradkin)--Vilkovisky (BV) and (BFV) framework for local Lagrangian field theory on manifolds possibly with boundary is discussed. Equivalence is phrased in…

In this paper we introduce the concept of Wiener-Luxemburg amalgam spaces which are a modification of the more classical Wiener amalgam spaces intended to address some of the shortcomings the latter face in the context of…

We characterize separable Banach spaces having $G_\delta$ isometry classes in the Polish codings $\mathcal{P}$, $\mathcal{P}_\infty$ and $\mathcal{B}$ introduced by C\'uth-Dole\v{z}al-Doucha-Kurka [13] as those being guarded Fra\"iss\'e, a…

Necessary and sufficient conditions for Banach space to be(isometrically isomorphic to) a dual space will be given.

The paper is a complement to the survey: M.I.Ostrovskii "To\-po\-lo\-gies on the set of all subspaces of a Banach space and related questions of Banach space geometry", Quaestiones Math. (to appear). It contains proofs of some results on…

The linear isometries between weighted Banach spaces of continuous functions are considered. Some of well known theorems on isometries between spaces of continuous functions are proved and stated, but all they are in an appropriate form. In…

This paper is concerned with complex Banach-space valued functions of the form $$ \hat{f}_k(r\cos\theta,r\sin\theta,z)=\mathrm{e}^{\mathrm{i} k \theta}f_k(r,z), \qquad r \in [0,\infty), \theta \in \mathbb{T}^1, z \in \mathbb{R}, $$ for some…

The main result says that every surjective isometry between two ideal Banach function spaces satisfying certain conditions can be presented as a composition of a measurable transformation of a variable and multiplication by a function.

Here we consider two notions of mappings of bounded variation (BV) from the metric measure space into the metric space; one based on relaxations of Newton-Sobolev functions, and the other based on a notion of AM-upper gradients. We show…

We construct a family of separable Hilbertian operator spaces, such that the relation of complete isomorphism between the subspaces of each member of this family is complete $\ks$. We also investigate some interesting properties of…

For $1\leq p\leq \infty$ and $\alpha>0$, Besov spaces $B^p_\alpha$ play a key role in the theory of $\alpha$-M\"obius invariant function spaces. In some sense, $B^1_\alpha$ is the minimal $\alpha$-M\"obius invariant function space,…

This article describes how the ideas promoted by the fundamental papers published by M. Frazier and B. Jawerth in the eighties have influenced subsequent developments related to the theory of atomic decompositions and Banach frames for…

For realcompact spaces X and Y we give a complete description of the linear biseparating maps between spaces of vector-valued continuous functions on X and Y, where special attention is paid to spaces of vector-valued bounded continuous…