Related papers: Rosenthal's space revisited

We consider conformal actions of simple Lie groups on compact Lorentzian manifolds. Mainly motivated by the Lorentzian version of a conjecture of Lichnerowicz, we establish the alternative: Either the group acts isometrically for some…

In the main result of the paper we extend Rosenthal's characterization of Banach spaces with the Schur property by showing that for a quasi-complete locally convex space $E$ whose separable bounded sets are metrizable the following…

For a separable rearrangement invariant space $X$ on $(0,\infty)$ of fundamental type we identify the set of all $p\in [1,\infty]$ such that $\ell^p$ is finitely represented in $X$ in such a way that the unit basis vectors of $\ell^p$…

We study the behavior of the normalized Ricci flow of invariant Riemannian homogeneous metrics at infinity for generalized Wallach spaces, generalized flag manifolds with four isotropy summands and second Betti number equal to one, and the…

In \cite{Roe} Roe proved that if a doubly-infinite sequence $\{f_k\}$ of functions on $\R$ satisfies $f_{k+1}=(df_{k}/dx)$ and $|f_{k}(x)|\leq M$ for all $k=0,\pm 1,\pm 2,...$ and $x\in \R$, then $f_0(x)=a\sin(x+\varphi)$ where $a$ and…

We consider generalizations of classical function spaces by requiring that a holomorphic in ${\Omega}$ function satisfies some property when we approach from ${\Omega}$, not the whole boundary, but only a part of it. These spaces endowed…

Certain previously known upper bounds on the moments of the norm of martingales in 2-smooth Banach spaces are improved. Some of these improvements hold even for sums of independent real-valued random variables. Applications to concentration…

Based on the work of Adams and Stuck as well as on the work of Zeghib, we classify the Lie groups which can act isometrically and locally effectively on Lorentzian manifolds of finite volume. In the case that the corresponding Lie algebra…

Let 1\leq p<2 and let L_p=L_p[0,1] be the classical L_p-space of all (classes of) p-integrable functions on [0,1]. It is known that a sequence of independent copies of a mean zero random variable f from L_p spans in L_p a subspace…

The main aim of this paper is to obtain Bochkarev-type inequalities for the anisotropic grand Lorentz spaces. In the classical setting, Bochkarev obtained inequalities of the Hardy--Littlewood type, which reveal the connection between the…

M\"untz spaces satisfying the M\"untz and gap conditions are considered. A Fourier approximation of functions in the M\"untz spaces $M_{\Lambda ,p}$ of $L_p$ functions is studied, where $1<p<\infty $. It is proved that up to an isomorphism…

Let $G$ be a compact subgroup of $GL_n(\R)$ acting linearly on a finite dimensional vector space $E$. B. Malgrange has shown that the space $\mathcal{C}^\infty(\R^n,E)^G$ of $\mathcal{C}^\infty$ and $G$-covariant functions is a finite…

By utilizing the idea of Colombeau's generalized function, we introduce a notion of asymptotic map between arbitrary diffeological spaces. The category consisting of diffeological spaces and asymptotic maps is enriched over the category of…

The paper introduces a variable exponent space $X$ which has in common with $L^{\infty}([0,1])$ the property that the space $C([0,1])$ of continuous functions on $[0,1]$ is a closed linear subspace in it. The associate space of $X$ contains…

The space of Lam\'e functions of order m is isomorphic to the space of pairs (elliptic curve, Abelian differential) where the differential has a single zero of order 2m at the origin and m double poles with vanishing residues. We describe…

Given a probability measure space $(X,\Sigma,\mu)$, it is well known that the Riesz space $L^0(\mu)$ of equivalence classes of measurable functions $f: X \to \mathbf{R}$ is universally complete and the constant function $\mathbf{1}$ is a…

This work builds on the foundation laid by Gordon and Wilson in the study of isometry groups of solvmanifolds, i.e. Riemannian manifolds admitting a transitive solvable group of isometries. We restrict ourselves to a natural class of…

We extend some results of Kwok-Pun Ho. In particular, it will be shown that every rearrangement-invariant quasi-Banach function space E on a totally sigma-finite measure space with a non-atomic measure can be expressed is the form…

We classify simply-connected homogeneous ($D+1$)-dimensional spacetimes for kinematical and aristotelian Lie groups with $D$-dimensional space isotropy for all $D\geq 0$. Besides well-known spacetimes like Minkowski and (anti) de Sitter we…

The rearrangement inequalities of Hardy-Littlewood and Riesz say that certain integrals involving products of two or three functions increase under symmetric decreasing rearrangement. It is known that these inequalities extend to integrands…