Related papers: Maximal Ergodic Inequalities for Banach Function S…

In this work we obtain a transference theorem for Lebesgue spaces with $A_{\infty }$ weights, namely, starting from some uniform-norm inequalities it is possible to obtain similar inequalities in Lebesgue spaces with $A_{\infty }$ weights.…

The robust statistical description of dynamical systems under perturbations is a central problem in ergodic theory. In this paper, we investigate the statistical properties of skew-product maps driven by a subshift of finite type with…

The aim of this paper is to study two-weight norm inequalities for fractional maximal functions and fractional Bergman operator defined on the upper-half space. Namely, we characterize those pairs of weights for which these maximal…

Let $X$ and $Y$ be Banach spaces such that the ideal of operators which factor through $Y$ has codimension one in the Banach algebra $\mathscr{B}(X)$ of all bounded operators on $X$, and suppose that $Y$ contains a complemented subspace…

In this paper, we study a class of Banach spaces, called \phi-spaces. In a natural way, we associate a measure of weak compactness in such spaces and prove an analogue of Sadovskii fixed point theorem for weakly sequentially continuous…

We first prove De Giorgi type level estimates for functions in $W^{1,t}(\Omega)$, $\Omega\subset\mathbb{R}^N$, with $t>N\geq 2$. This augmented integrability enables us to establish a new Harnack type inequality for functions which do not…

We study the convergence of the so-called entangled ergodic averages $\frac{1}{N^k}\sum_{n_1,...,n_k=1}^{N}T_m^{n_{\alpha(m)}}A_{m-1}T_{m-1}^{n_{\alpha(m-1)}}A_{m-2}...A_1T_1^{n_{\alpha(1)}},$ where $k\leq m$ and…

In a companion article we have introduced a notion of multiscale functional inequalities for functions $X(A)$ of an ergodic stationary random field $A$ on the ambient space $\mathbb R^d$. These inequalities are multiscale weighted versions…

Greedy algorithms which use only function evaluations are applied to convex optimization in a general Banach space $X$. Along with algorithms that use exact evaluations, algorithms with approximate evaluations are treated. A priori upper…

In this paper we investigate the spectra and the ergodic properties of the multiplication operators and the convolution operators acting on the Schwartz space $\mathcal{S}(\mathbb{R})$ of rapidly decreasing functions, i.e., operators of the…

Geodesic contraction in vector-valued differential equations is readily verified by linearized operators which are uniformly negative-definite in the Riemannian metric. In the infinite-dimensional setting, however, such analysis is…

In this paper we study aspects of the ergodic theory of the geodesic flow on a non-compact negatively curved manifold. It is a well known fact that every continuous potential on a compact metric space has a maximizing measure.…

We prove some results on weakly almost square Banach spaces and their relatives. On the one hand, we discuss weak almost squareness in the setting of Banach function spaces. More precisely, let $(\Omega,\Sigma)$ be a measurable space, let…

In this paper we prove a general form of the Mass Transference Principle for $\limsup$ sets defined via neighbourhoods of sets satisfying a certain local scaling property. Such sets include self-similar sets satisfying the open set…

The existence of a Banach limit as a translation invariant positive continuous linear functional on the space of bounded scalar sequences which is equal to 1 at the constant sequence (1,1,...,1,...) is proved in a first course on functional…

Existence and uniqueness as well as the iterative approximation of fixed points of enriched almost contractions in Banach spaces are studied. The obtained results are generalizations of the great majority of metric fixed point theorems, in…

We investigate whether almost weak stability of an operator $T$ on a Banach space $X$ implies its almost weak polynomial stability. We show, using a modified version of the van der Corput Lemma that if $X$ is a Hilbert space and $T$ a…

This paper is devoted to the study of noncommutative ergodic theorems for connected amenable locally compact groups. For a dynamical system $(\mathcal{M},\tau,G,\sigma)$, where $(\mathcal{M},\tau)$ is a von Neumann algebra with a normal…

Let $T$ be a bounded linear operator on a Banach space $X$ satisfying $\|T^n\|/n \to 0$. We prove that $T$ is uniformly ergodic if and only if the one-sided ergodic Hilbert transform $H_Tx:= \lim_{n\to\infty} \sum_{k=1}^n k^{-1}T^k x$…

We establish a weighted inequality for fractional maximal and convolution type operators, between weak Lebesgue spaces and Wiener amalgam type spaces on $ \mathbb R $ endowed with a measure which needs not to be doubling.