Related papers: A noncommutative weak type maximal inequality for …

In this article, we consider weighted weak type $(1,1)$ inequality for certain square function associated to differences of ball averages and martingale in the non-commutative setting. This establishes a weighted version of main result of…

Let $n\ge 2$ be the spatial dimension. The purpose of this note is to obtain some weighted estimates for the fractional maximal operator ${\mathfrak M}{\alpha}$ of order $\alpha$, $0\le\alpha<n$, on the weighted Choquet-Lorentz space…

We prove that any weak* continuous semigroup $(T_t)_{t \geq 0}$ of factorizable Markov maps acting on a von Neumann algebra $M$ equipped with a normal faithful state can be dilated by a group of Markov $*$-automorphisms analogous to the…

We consider operators $T$ satisfying a sparse domination property \[ |\langle Tf,g\rangle|\leq c\sum_{Q\in\mathscr{S}}\langle f\rangle_{p_0,Q}\langle g\rangle_{q_0',Q}|Q| \] with averaging exponents $1\leq p_0<q_0\leq\infty$. We prove…

The general affine group $G_n$ sits at the intersection of harmonic analysis on solvable groups and the geometry of negatively curved symmetric spaces. In this work, we characterize the $L^p$-behavior of maximal operators associated with…

In the paper we consider Calder\'{o}n-Zygmund operators in nonhomogeneous spaces. We are going to prove the analogs of classical results for homogeneous spaces. Namely, we prove that a Calder\'{o}n-Zygmund operator is of weak type if it is…

We consider the following class of mixed local-nonlocal equations: \begin{align}\label{abs}\tag{$\mathcal{P}$} -\Delta_p u + (-\Delta)_p^s u = V |u|^{p-2}u \text{ in } \Omega, \end{align} where $s \in (0,1), p \in (1, \infty)$, and the…

Let $v,~\omega_1, ~\omega_2$ be weights and $1<p_1, ~p_2<\infty.$ Suppose that $\frac{1}{p}=\frac{1}{p_1}+\frac{1}{p_2}$ and $(\omega_1, \omega_2)\in RH(p_1, p_2).$ For the multisublinear maximal operator $\mathfrak{M}$ in martingale…

As shown in [A1], the lowest constants appearing in the weak type (1,1) inequalities satisfied by the centered Hardy-Littlewood maximal operator associated to certain finite radial measures, grow exponentially fast with the dimension. Here…

It is shown that the cubic nonconventional ergodic averages of any order with a bounded aperiodic multiplicative function or von Mangoldt weights converge almost surely.

We provide explicit examples of positive and power-bounded operators on $c_0$ and $\ell^\infty$ which are mean ergodic but not weakly almost periodic. As a consequence we prove that a countably order complete Banach lattice on which every…

Local mean and individual (with respect to almost uniform convergence in Egorov's sense) ergodic theorems are established for actions of the semigroup $\mathbb R_+^d$ in symmetric spaces of measurable operators associated with a semifinite…

\begin{abstract} For the Hardy space $H^p(\mathbb{R}^{d})$, $ 0<p\leq 1,$ we shall improve a Hardy's type inequality associated with Dunkl transform respect to the measures $d\mu_{k}$ homogeneous of degree $\gamma ,$ on the strip…

The Birkhoff Ergodic Theorem concludes that time averages, i.e., Birkhoff averages, $\Sigma_{n=0}^{N-1} f(x_n)/N$ of a function $f$ along a length $N$ ergodic trajectory $(x_n)$ of a function $T$ converge to the space average $\int f d\mu$,…

In this paper, we prove strong type, weak type inequalities of Hardy-Littlewood maximal operator and fractional Hardy-Littlewood maximal operator on variable sequence spaces lp(Z). This is achieved using Calderon-Zygmund decomposition for…

Suppose that T_t is a symmetric diffusion semigroup on L^2(X) and consider its tensor product extension to the Bochner space L^p(X,B), where B belongs to a certain broad class of UMD spaces. We prove a vector-valued version of the…

We prove that the Hardy--Littlewood maximal operator $M$ is bounded on the variable Lebesgue space $L^{p(\cdot)}(X,d,\mu)$, with $1<p_-\le p_+<\infty$, over an unbounded space of homogeneous type $(X,d,\mu)$ with a Borel-semiregular measure…

In this paper, we present a sufficient condition on a pair of nonnegative weights $v$ and $w$ such that we have a general weighted $L^{p}$-Hardy type identity. The result, for a certain choice of weights, gives weighted $L^{p}$-Hardy type…

Let $1\leq p <\infty$ and $0 < q,r < \infty$. We characterize the validity of the inequality for the composition of the Hardy operator, \begin{equation*} \bigg(\int_a^b \bigg(\int_a^x \bigg(\int_a^t f(s)ds \bigg)^q u(t) dt…

We characterize a three-weight inequality for an iterated discrete Hardy-type operator. In the case when the domain space is a weighted space $\ell^p$ with $p\in(0,1]$, we develop characterizations which enable us to reduce the problem to…