Related papers: On the commutation of generalized means on probabi…

Let X be a countably infinite set, and let f, g, and h be any three injective self-maps of X, each having at least one infinite cycle. (For instance, this holds if f, g, and h are not bijections.) We show that there are permutations a and b…

We generalise a result of Hedenmalm to show that if a function $f$ on $\mathbb{R}$ is such that $\int_{\mathbb{R}^2} \bigl|f(x) \, \hat f(y)\bigr| \,e^{\lambda \left|xy\right|} \,dx\,dy = O( (1-\lambda)^{-N} )$ as $\lambda \to 1-$, then $f$…

In this paper, we will obtain the strong type and weak type estimates for vector-valued analogues of intrinsic square functions in the generalized weighted Morrey spaces $M^{\Phi,\varphi}_{w}(\mathbb{R}^n)$. We study the boundedness of…

We study a model of spatial random permutations over a discrete set of points. Formally, a permutation $\sigma$ is sampled proportionally to the weight $\exp\{-\alpha \sum_x V(\sigma(x)-x)\},$ where $\alpha>0$ is the temperature and $V$ is…

Let $\mu$ be the Haar measure of a unimodular locally compact group $G$ and $m (G)$ as the infimum of the volumes of all open subgroups of $G$. The main result of this paper is that \begin{align*} \int_{G}^{} f \circ \left( \phi_1 * \phi_2…

Let a sequence of iid. random variables $\xi_1,...,\xi_n$ be given on a measurable space $(X,\cal X)$ with distribution $\mu$ together with a function $f(x_1,...,x_k)$ on the product space $(X^k,{\cal X}^k)$. Let $\mu_n$ denote the…

We present a novel proof of de Finetti's Theorem characterizing permutation-invariant probability measures of infinite sequences of variables, so-called exchangeable measures. The proof is phrased in the language of Markov categories, which…

Let $f,g:\Bbb{R}^{N}\rightarrow (-\infty ,\infty ]$ be Borel measurable, bounded below and such that $\inf f+\inf g\geq 0.$ We prove that with $ m_{f,g}:=(\inf f-\inf g)/2,$ the inequality $||(f-m_{f,g})^{-1}||_{\phi…

We consider a pair of probability measures $\mu,\nu$ on the unit circle such that $\Sigma_{\lambda}(\eta_{\nu}(z))=z/\eta_{\mu}(z)$. We prove that the same type of equation holds for any $t\geq 0$ when we replace $\nu$ by…

Let $G$ be a real Lie group, $\Lambda<G$ a lattice and $H<G$ a connected semisimple subgroup without compact factors and with finite center. We define the notion of $H$-expanding measures $\mu$ on $H$ and, applying recent work of…

Let $L$ be a second order elliptic operator on $R^d$ with a constant diffusion matrix and a dissipative (in a weak sense) drift $b \in L^p_{loc}$ with some $p>d$. We assume that $L$ possesses a Lyapunov function, but no local boundedness of…

Let (L,\preccurlyeq) be a finite distributive lattice, and suppose that the functions f_1,f_2:L\to R are monotone increasing with respect to the partial order \preccurlyeq. Given \mu a probability measure on L, denote by E(f_i) the average…

Let G be a locally compact group L^p(G) be the usual L^p-space for 1 =< p =< infty and A(G) be the Fourier algebra of G. Our goal is to study, in a new abstract context, the completely bounded multipliers of A(G), which we denote…

For each $\lambda \in \mathbb N^*$, we consider the integral equation: \[ \int_{\lambda y} ^{\lambda x} f(t)\, d t = f(x) - f(y) \mbox{ for every $(x,y)\in {\mathbb R}_+^2$,} \] where $f$ is the concatenation of two continuous functions…

The paper provides a complement to the classical results on Fourier multipliers on $L^p$ spaces. In particular, we prove that if $q\in (1,2)$ and a function $m:\mathbb{R} \rightarrow \mathbb{C}$ is of bounded $q$-variation uniformly on the…

Let $\Omega\subsetneq\mathbb R^{n+1}$ be open and let $\mu$ be some measure supported on $\partial\Omega$ such that $\mu(B(x,r))\leq C\,r^n$ for all $x\in\mathbb R^{n+1}$, $r>0$. We show that if the harmonic measure in $\Omega$ satisfies…

Let $(\mathcal{X},\mathcal{F},\mu)$ and $(\mathcal{Y},\mathcal{G},\nu)$ be probability spaces and $(Z_n)$ a sequence of random variables with values in $(\mathcal{X}\times\mathcal{Y},\,\mathcal{F}\otimes\mathcal{G})$. Let $\Gamma(\mu,\nu)$…

The purpose of this paper is to investigate the local and global comparison of two $n$-variable generalized Bajraktarevi\'c means, i.e., to establish necessary as well as sufficient conditions in terms of the unknown functions…

We consider the dynamical system given by a diagonalizable element $a$ of a closed linear unimodular algebraic subgroup $G$ of the special linear group over the $p$-adic numbers acting by translation on a finite volume quotient $X$.…

A space of pseudoquotients $\mathcal P (X,S)$ is defined as equivalence classes of pairs $(x,f)$, where $x$ is an element of a non-empty set $X$, $f$ is an element of $S$, a commutative semigroup of injective maps from $X$ to $X$, and…