Related papers: Commutators of vector-valued intrinsic square func…

We study the boundedness of commutators of the Hardy-Littlewood maximal function and the sharp maximal function on weighted Morrey spaces when the symbols of the commutators belong to weighted Lipschitz spaces. Some new characterizations…

In the setting of homogeneous spaces (X,d,{\mu}), it is shown that the commutator of Calder\'on- Zygmund type operators as well as commutator of potential operator with BMO function are bounded in generalized Grand Morrey space. Interior…

Let $p(\cdot):\ \mathbb R^n\to(0,\infty)$ be a measurable function satisfying some decay condition and some locally log-H\"older continuity. In this article, via first establishing characterizations of the variable exponent Hardy space…

Let $T_m$ be the $m$-th Calder\'on-Zygmund type singular integral. In the paper, we consider the boundedness of $T_m$ on the generalized product local Morrey spaces $LM_{p_1,\varphi_1}^{\{x_0\}}\times…

Let $T$ be a Calder\'on-Zygmund singular integral operator. In this paper, we will show some weighted boundedness properties of commutator $[b,T]$ on the weighted Morrey spaces $L^{p,\kappa}(w)$ under appropriate conditions on the weight…

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…

We consider generalized Orlicz-Morrey spaces $M_{\Phi,\varphi}(\Rn)$ including their weak versions $WM_{\Phi,\varphi}(\Rn)$. In these spaces we prove the boundedness of the Riesz potential from $M_{\Phi,\varphi_1}(\Rn)$ to…

This paper is devoted to studying the boundedness of multilinear operartors and their commutators on generalized weighted Morrey spaces, which includes multilinear fractional maximal operator and multilinear fractional integral operator.…

Let $L$ be the infinitesimal generator of an analytic semigroup on $L^2(R^n)$ with Gaussican kernel bounds, and let $L^{-\alpha/2}$ be the fractional integrals of $L$ for $0<\alpha<n.$ For any locally integrable function $b$, The…

In this paper, the author studies the boundedness for a large class of sublinear operator $T_\alpha, \alpha\in[0,n)$ generated by Calder{\'o}n-Zygmund operators ($\alpha=0$) and generated by fractional integral operator ($\alpha>0$) on…

We prove sharp $L^p(w)$ norm inequalities for the intrinsic square function (introduced recently by M. Wilson) in terms of the $A_p$ characteristic of $w$ for all $1<p<\infty$. This implies the same sharp inequalities for the classical…

In this paper, we introduce a type of weighted multilinear Hardy operators and obtain their sharp bounds on the product of Lebesgue spaces and central Morrey spaces. In addition, we obtain sufficient and necessary conditions of the weight…

In this paper, we will study the boundedness of intrinsic square functions on the weighted Hardy spaces $H^p(w)$ for $0<p<1$, where $w$ is a Muckenhoupt's weight function. We will also give some intrinsic square function characterizations…

The aim of this paper is to obtain the boundedness of some operator on grand generalized weighted Morrey spaces $\mathcal{L}^{p),\phi}_{\varphi}(\omega)$ over RD-spaces. Under assumption that functions $\varphi$ and $\phi$ satisfy certain…

Let $L$ be the infinitesimal generator of an analytic semigroup on $L^2(\mathbb R^n)$ with Gaussian kernel bound, and let $L^{-\alpha/2}$ be the fractional integrals of $L$ for $0<\alpha<n$. In this paper, we will obtain some boundedness…

In this article we obtain the characterization for the commutators of maximal functions on the weighted Morrey spaces in the setting of spaces of homogeneous type. More precisely, we characterize BMO spaces using the commutators of…

We investigate $g$-functions and Lusin's area type integrals related to certain multi-dimensional Dunkl and Laguerre settings. We prove that the considered square functions are bounded on weighted $L^p$, $1<p<\infty$, and from $L^1$ into…

In this paper we investigate the boundedness of sublinear operators generated by fractional integrals as well as sublinear operators generated by Calder\`on-Zygmund operators on generalized weighted Morrey spaces and generalized weighted…

Let $\mathcal{M}$ be the bilinear Hardy-Littlewood maximal function and $\vec{b}=(b,b)$ be a collection of locally integrable functions. In this paper, the authors establish characterizations of the weighted {\rm BMO} space in terms of…

This paper investigates the boundedness of a broad class of operators within the framework of generalized Morrey-Banach function spaces. This class includes multilinear operators such as multilinear $\omega$-Calder\'{o}n-Zygmund operators,…