Related papers: The boundedness of some operators with rough kerne…

In this paper, we will study the boundedness properties of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and $g^*_\lambda$-function on the weighted Morrey spaces $L^{p,\kappa}(w)$ for…

In this paper, we will study the boundedness properties of multilinear Calderon--Zygmund operators and multilinear fractional integrals on products of weighted Morrey spaces with multiple weights.

Let $\delta\in(0,1]$ and $T$ be a $\delta$-Calder\'on-Zygmund operator. Let $w$ be in the Muckenhoupt class $A_{1+\delta/n}({\mathbb R}^n)$ satisfying $\int_{{\mathbb R}^n}\frac {w(x)}{1+|x|^n}\,dx<\infty$. When $b\in{\rm BMO}(\mathbb…

In this paper, we study the boundedness theory for maximal Calder\'on-Zygmund operators acting on noncommutative $L_p$-spaces. Our first result is a criterion for the weak type $(1,1)$ estimate of noncommutative maximal Calder\'on-Zygmund…

Let $0\leq \alpha<n$, $m\in \mathbb{N}$ and let consider $T_{\alpha,m}$ be a of integral operator, given by kernel of the form $$K(x,y)=k_1(x-A_1y)k_2(x-A_2y)\dots k_m(x-A_my),$$ where $A_i$ are invertible matrices and each $k_i$ satisfies…

In this paper, we establish the sharp boundedness of p-adic multilinear Hausdorff operators on the product of Lebesgue and central Morrey spaces associated with both power weights and Muckenhoupt weights. Moreover, the boundedness for the…

In this article we introduce a stochastic counterpart of the H\"ormander condtion on the kernel $K(r,t,x,y)$: there exists a pseudo-metric $\rho$ on $(0,\infty)\times R^d$ and a positive constant $C_0$ such that for $X=(t,x), Y=(s,y),…

In this article, we introduce a class of multilinear strongly singular integral operators with generalized kernels on the RD-space. The boundedness of these operators on weighted Lebesgue spaces is established. Moreover, two types of…

We obtain the optimal open range of $L^{p_1}(\mathbb R^n)\times\cdots\times L^{p_m}(\mathbb R^n)\to L^p(\mathbb R^n)$ bounds for multilinear singular integral operators with homogeneous kernels of the form $\Omega(\frac{y}{|y|})|y|^{-mn}$,…

Let $X$ be a ball Banach function space on ${\mathbb R}^n$. Let $\Omega$ be a Lipschitz function on the unit sphere of ${\mathbb R}^n$,which is homogeneous of degree zero and has mean value zero, and let $T_\Omega$ be the convolutional…

Let $({\mathcal X},\,d,\,\mu)$ be a metric measure space satisfying the upper doubling condition and the geometrically doubling condition in the sense of T. Hyt\"onen. In this paper, the authors prove that the $L^p(\mu)$ boundedness with…

This paper is devoted to establishing the kernel theorems for $\alpha$-modulation spaces in terms of boundedness and compactness. We characterize the boundedness of a linear operator $A$ from an $\alpha$-modulation space…

Motivated by the study of kernels of bilinear pseudodifferential operators with symbols in a H\"ormander class of critical order, we investigate boundedness properties of strongly singular Calder\'on--Zygmund operators in the bilinear…

Let $T$ be a bilinear Calder\'on-Zygmund singular integral operator and $T^*$ be its corresponding truncated maximal operator. For any $b\in\text{BMO}(\mathbb {R}^n)$ and $\vec{b}=(b_1,\ b_2)\in\text{BMO}(\mathbb {R}^n)\times\text…

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…

Let $[b,\mathcal T_\alpha]~(0\leq\alpha<n)$ be the commutators generated by $BMO(\mathbb R^n)$ functions and a class of sublinear operators satisfying certain size conditions. The aim of this paper is to study the endpoint estimates of…

Let $T_1$, $T_2$ be two singular integral operators with nonsmooth kernels introduced by Duong and McIntosh. In this paper, by establishing certain bi-sublinear sparse domination, the authors obtain some quantitative bounds on…

In this paper, the authors define the mixed $\lambda$-central Morrey spaces and the mixed $\lambda$-central $BMO$ spaces. The boundedness of the fractional integral operators $T_{\alpha}$ and its commutators $[b, T_{\alpha}]$ are…

Weighted $L^p-L^r$ inequalities with arbitrary measurable non-negative weights for positive quasilinear integral operators with Oinarov's kernel on the semiaxis are characterized. Application to the boundedness of maximal operator in the…

We shall investigate the boundedness of the intrinsic square functions and their commutators on generalized weighted Orlicz-Morrey spaces $M^{\Phi,\varphi}_{w}({\mathbb R}^n)$. In all the cases, the conditions for the boundedness are given…