Related papers: Maximal Ergodic Theorem On Weighted $L^p_w(X)$ spa…
We construct new optimal $L^p$ Hardy-type inequalities for elliptic Schr\"odinger-type operators
In this paper, we first give some new characterizations of Muckenhoupt type weights through establishing the boundedness of maximal operators on the weighted Lorentz and Morrey spaces. Secondly, we establish the boundedness of sublinear…
Let $T$ be an ergodic measure-preserving transformation on a non-atomic probability space $(X,\Sigma,\mu)$. We prove uniform extensions of the Wiener-Wintner theorem in two settings: For averages involving weights coming from Hardy field…
For ergodic optimization on any topological dynamical system, with real-valued potential function $f$ belonging to any separable Banach space $B$ of continuous functions, we show that the $f$-maximizing measure is typically unique, in the…
We analyse the Transfer Principle, which is used to generate weak type maximal inequalities for ergodic operators, and extend it to the general case of $\sigma$-compact locally compact Hausdorff groups acting measure-preservingly on…
It is known that, for a positive Dunford-Schwartz operator in a noncommutative $L^p-$space, $1\leq p<\infty$ or, more generally, in a noncommutative Orlicz space with order continuous norm, the corresponding ergodic averages converge…
We show that if $(X, \mu, T)$ is a probability measure-preserving dynamical system, and $\mathscr{P}$ is a countable partition of $(X, \mu)$, then the limit $$ \lim_{n, k \to \infty} \mathbb{E} \left[ \frac{1}{k} \sum_{j = 0}^{k - 1} f…
We extend an $L^2$ maximal multiplier result of Bourgain to all $L^p$ spaces, $1<p<\infty$.
We prove the mean ergodic theorem of von Neumann in a Hilbert-Kaplansky space. We also prove a multiparameter, modulated, subsequential and a weighted mean ergodic theorems in a Hilbert-Kaplansky space
In this article, we establish maximal inequalities and deduce ergodic theorems for state-preserving actions of amenable, locally compact, second-countable groups on tracial non-commutative $L^1$-spaces. As a further consequence, in…
The fundamental aim of this paper is to define weighted q-Hardy-littlewood-type maximal operator by means of fermionic p-adic q-invariant distribution on Zp . Also, we derive some interesting properties concerning this type maximal…
It is known that, for a positive Dunford-Schwartz operator in a noncommutative $L^p-$space, $1\leq p<\infty$ or, more generally, in a noncommutative Orlicz space with order continuous norm, the corresponding ergodic averages converge…
The main goal of this note is to show that (not necessarily holomorphic) multipliers of a wide class of normed spaces of continuous functions over a connected Hausdorff topological space cannot attain their multiplier norms, unless they are…
We present a complete characterization of the metric compactification of $L_{p}$ spaces for $1\leq p < \infty$. Each element of the metric compactification of $L_{p}$ is represented by a random measure on a certain Polish space. By way of…
The essential aim of this paper is to define weighted q-Hardy-littlewood-type maximal operator by means of p-adic q-invariant distribution on Zp. Moreover, we give some interesting properties concerning this type maximal operator.
In this paper, we prove $L^p$ ($p > 1$) dimension free bounds for the centered Hardy-Littlewood maximal function on real or complex hyperbolic spaces.
In \cite{MR447956}, Muckenhoupt and Wheeden formulated a weighted weak $(p,p)$ inequality where the weight for the weak $L^p$ space is treated as a multiplier rather than a measure. They proved such inequalities for the Hardy-Littlewood…
Let $X$ be a compact complex surface. Consider a finitely supported probability measure $\mu$ on $\text{Aut}(X)$ such that $\Gamma_{\mu} = \langle \text{Supp}(\mu)\rangle<\text{Aut}(X)$ is non-elementary. We do not assume that…
We study the arithmetic analogue of maximal functions on diagonal hypersurfaces. This paper is a natural step following the papers of \cite{Magyar_dyadic}, \cite{Magyar_ergodic} and \cite{MSW}. We combine more precise knowledge of…
Recently, Auscher and Axelsson gave a new approach to non-smooth boundary value problems with $L^{2}$ data, that relies on some appropriate weighted maximal regularity estimates. As part of the development of the corresponding $L^{p}$…