Related papers: $L^T_p-$ functions on locally compact groups

Traditional Lp spaces are fundamental in functional analysis, demarcated by the relationship $1/p + 1/q = 1$. This research pioneers the concept of $\theta$-Lebesgue space, stemming from a simultaneous weakening of both the classical $L_p$…

We give an affirmative answer to a question due to M. Megrelishvili, and show that for every locally compact group $G$ we have $\operatorname{Tame}(L^{1}(G)) = \operatorname{Tame}(G)$, which means that a functional is tame over $L^{1}(G)$…

We provide a general treatment of perturbations of a class of functionals modeled on convolution energies with integrable kernel which approximate the $p$-th norm of the gradient as the kernel is scaled by letting a small parameter…

We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also…

In the paper we look for an elegant proof of the characterization of relatively compact families in $L^p-$spaces. At first glance, the suggested approach may seem convoluted and lengthy, but we spare no effort to argue that our proof is in…

We study the $L^p$-spectrum of the Laplace-Beltrami operator on certain complete locally symmetric spaces $M=\Gamma\backslash X$ with finite volume and arithmetic fundamental group $\Gamma$ whose universal covering $X$ is a symmetric space…

In the present note we introduce tame functionals on Banach algebras. A functional $f \in A^*$ on a Banach algebra $A$ is tame if the naturally defined linear operator $A \to A^*, a \mapsto f \cdot a$ factors through Rosenthal Banach spaces…

Let $G$ be a locally compact group, $\mu$ its Haar measure, $\hat G$ its Pontryagin dual and $\nu$ the dual measure. For any $A_\theta\in L^1(G;\mathcal C_p)\cap L^2(G;\mathcal C_p)$, ($\mathcal C_p$ is Schatten ideal), and $1<p\le2$ we…

A new class of groups, the locally finitely determined groups of local similarities on compact ultrametric spaces, is introduced and it is proved that groups in this class have the Haagerup property (that is, they are a-T-menable in the…

We introduce and investigate using Hilbert modules the properties of the {\em Fourier algebra} $A(G)$ for a locally compact groupoid $G$. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This…

In this article we give a counter-example on the statement of a theorem appearing in a note $[3]$ of A. Brunel concerning the study of positive operators on the the spaces $L_p\,\,(1<p<\infty)$ which the sequence of the powers is…

Let $\Gamma$ be a graph equipped with a Markov operator $P$. We introduce discrete fractional Littlewood-Paley square functionals and prove their $L^p$-boundedness under various geometric assumptions on $\Gamma$.

We give a new proof of a recent characterization by Diaz and Mayoral of compactness in the Lebesgue-Bochner spaces $L_X^p$, where $X$ is a Banach space and $1\le p<\infty$, and extend the result to vector-valued Banach function spaces…

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…

Given a locally compact group $G$ and $1\leq p<\infty$, a sufficient condition ensuring the \emph{disjoint hypercyclicity} of finitely many weighted translations on $L^p(G)$ was investigated in this paper.

We announce various results concerning the structure of compactly generated simple locally compact groups. We introduce a local invariant, called the structure lattice, which consists of commensurability classes of compact subgroups with…

We discuss the finiteness of the topological entropy of continuous endomorphims for some classes of locally compact groups. Firstly, we focus on the abelian case, imposing the condition of being compactly generated, and note an interesting…

In this paper local polynomials on Abelian groups are characterized by a "local" Fr\'echet-type functional equation. We apply our result to generalize Montel's Theorem and to obtain Montel-type theorems on commutative groups.

Extending and unifying concepts extensively used in the literature, we introduce the notion of approximable interpolation sets for algebras of functions on locally compact groups, especially for weakly almost periodic functions and for…

We study the group $C^*$-algebras $C^*_{L^{p+}}(G)$ - constructed from $L^p$-integrability properties of matrix coefficients of unitary representations - of locally compact groups $G$ acting on (semi-)homogeneous trees of sufficiently large…