Related papers: Weighted Norm Inequalities for Parametric Littlewo…

For the Hardy-Littlewood maximal and Calder\'on-Zygmund operators, the weighted boundedness on the Lebesgue spaces are well known. We extend these to the Orlicz-Morrey spaces. Moreover, we prove the weighted boundedness on the weak…

Let $X$ be a space of homogeneous type. Assume that $L$ is an non-negative second-order self-adjoint operator on $L^2\left(X\right)$ with (heart) kernel associated to the semigroup $e^{ - tL}$ that satisfies the Gaussian upper bound. In…

In this paper, we prove the boundedness of the multilinear Littlewood-Paley square operators and their commutators on weighted Morrey spaces, then we give the boundedness and weak-type $L\log L$ estimates for the commutators of multilinear…

In this note we consider weighted conditional type operators between different Orlicz spaces and generalized conditional type Holder inequality that we defined in [2]. Then we give some necessary and sufficient conditions for boundedness of…

In this paper, by using the atomic decomposition theory of Hardy space and weak Hardy space, we discuss the boundedness of parameterized Littlewood-Paley operator with variable kernel on these spaces.

In this paper, we consider the predual spaces of weak Orlicz spaces. As an application, we provide the Fefferman-Stein vector-valued maximal inequality for the weak Orlicz spaces. In order to prove this statement, we introduced the…

The main goal of this paper is to provide a complete characterization of the weak-type boundedness of the Hardy-Littlewood maximal operator, $M$, on weighted Lorentz spaces $\Lambda^p_u(w)$, whenever $p>1$. This solves a problem left open…

We give weighted norm inequalities for the maximal fractional operator $ \mathcal M_{q,\beta}$ of Hardy-Littlewood and the fractional integral $I_{\gamma}$. These inequalities are established between $(L^{q},L^{p}) ^{\alpha}(X,d,\mu)$…

In this paper, the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue spaces to Orlicz spaces are obtained. The operators include Calder\'on--Zygmund singular integral operator,…

In this paper, we obtain the necessary and sufficient conditions for the weak/strong boundedness of the Calder\'{o}n-Zygmund operators in generalized weighted Orlicz-Morrey spaces. We also study the boundedness of the commutators of…

Let $(\Omega,\mathcal{F},\mathbb{P})$ be a probability space and $\varphi:\ \Omega\times[0,\infty)\to [0,\infty)$ be a Musielak--Orlicz function. In this article, the authors establish the atomic characterizations of weak martingale…

In this paper, we investigate necessary and sufficient conditions on the boundedness of composition operators on the Orlicz-Morrey spaces. The results of boundedness include Lebesgue and generalized Morrey spaces as special cases. Further,…

Let $t\in(0,\infty)$, $p\in(1,\infty)$, $q\in[1,\infty]$, $w\in A_p$ and $v\in A_q$. We introduce the weighted amalgam space $(L^p,L^q)_t(\mathbb R^n)$ and show some properties of it. Some estimates on these spaces for the classical…

In this paper we investigate the boundedness of classical operators, namely the Hardy-Littlewood maximal operator, fractional integral operators, and Calderon-Zygmund operators, on generalized weighted Morrey spaces and generalized weighted…

In this paper, we first obtain the operator norms of the $n$-dimensional Hardy-Littlewood-P\'{o}lya operator $\mathcal{H}$ from weighted Lebesgue spaces $L^p( \mathbb{R} ^n,| x |^{\beta} ) $ to weighted weak Lebesgue spaces…

We study the boundedness of some sublinear operators on weighted Morrey spaces under certain size conditions. These conditions are satisfied by most of the operators in harmonic analysis, such as the Hardy-Littlewood maximal operator,…

Let $\varphi:\mathbb{R}^n\times[0,\,\infty) \rightarrow [0,\,\infty)$ satisfy that $\varphi(x,\,\cdot)$, for any given $x\in\mathbb{R}^n$, is an Orlicz function and $\varphi(\cdot\,,t)$ is a Muckenhoupt $A_\infty$ weight uniformly in…

In this article, the authors first introduce a class of Orlicz-slice spaces which generalize the slice spaces recently studied by P. Auscher et al. Based on these Orlicz-slice spaces, the authors introduce a new kind of Hardy type spaces,…

In this paper, by introducing some parameters, we define and study certain $p$-adic Hardy-Littlewood-P\'{o}lya-type integral operators acting on $p$-adic weighted Lebesgue spaces. We completely characterize $L^{q}-L^{r}$ boundedness of…

To appear in J. Funct. Spaces and Appl.