相关论文: Boundedness of Lusin-area and $g_\lambda^\ast$ Fun…

In this paper, we characterize Bounded Mean Oscillation (BMO) and establish their connection with Hankel operators on weighted Bergman spaces over tubular domains. By utilizing the space BMO, we provide a new characterization of Bloch…

Let $G$ be a locally compact abelian metric group with Haar measure $\lambda $ and $\hat{G}$ its dual with Haar measure $\mu ,$ and $\lambda ( G) $ is finite. Assume that$~1<p_{i}<\infty $, $p_{i}^{\prime }=\frac{ p_{i}}{p_{i}-1}$, $(…

Let $X$ be a ball quasi-Banach function space on ${\mathbb R}^n$ and $H_X({\mathbb R}^n)$ the Hardy space associated with $X$, and let $\alpha\in(0,n)$ and $\beta\in(1,\infty)$. In this article, assuming that the (powered) Hardy--Littlewood…

In this paper we consider square functions (also called Littlewood-Paley g-functions) associated to Hankel convolutions acting on functions in the Bochner-Lebesgue space $L^p((0,\infty),B)$, where $B$ is a UMD Banach space. As special cases…

Let $d\gamma(x)\equiv\pi^{-n/2}e^{-|x|^2}dx$ for all $x\in{\mathbb R}^n$ be the Gauss measure on ${\mathbb R}^n$. In this paper, the authors establish the characterizations of the space BMO$(\gamma)$ of Mauceri and Meda via commutators of…

By employing the differential structure recently developed by N. Gigli, we first give a notion of functions of bounded variation ($BV$) in terms of suitable vector fields on a complete and separable metric measure space $(\mathbb{X},d,\mu)$…

We introduce a Cherednik kernel and a hypergeometric function for integral root systems and prove their relation to spherical functions associated with Riemannian symmetric spaces of reductive Lie groups. Furthermore, we characterize the…

Let $A_1$ and $A_2$ be expansive dilations, respectively, on ${\mathbb R}^n$ and ${\mathbb R}^m$. Let $\vec A\equiv(A_1, A_2)$ and $\mathcal A_p(\vec A)$ be the class of product Muckenhoupt weights on ${\mathbb R}^n\times{\mathbb R}^m$ for…

Let $({\mathcal X}, d, \mu)$ be a metric measure space and satisfy the so-called upper doubling condition and the geometrically doubling condition. In this paper, the authors introduce the space ${\mathop\mathrm{RBLO}}(\mu)$ and prove that…

We prove that for any homogeneous, second order, constant complex coefficient elliptic system $L$, the Dirichlet problem in $\mathbb{R}^{n}_{+}$ with boundary data in BMO is well-posed in the class of functions $u$ with…

Let $T(f)$ denote the Littlewood--Paley square operators, including the Littlewood--Paley $\mathcal{G}$-function $\mathcal{G}(f)$, Lusin's area integral $\mathcal{S}(f)$ and Stein's function $\mathcal{G}^{\ast}_{\lambda}(f)$ with…

Let $m,n\ge 1$ and $g_{\lambda_1,\lambda_2}^*$ be the bi-parameter Littlewood-Paley $g_{\lambda}^{*}$-function defined by $$ g_{\lambda_1,\lambda_2}^*(f)(x)= \bigg(\iint_{\R^{m+1}_{+}} \big(\frac{t_2}{t_2 + |x_2 - y_2|}\big)^{m \lambda_2}…

We first consider two types of localizations of singular integral operators of convolution type, and show, under mild decay and smoothness conditions on the auxiliary functions, that their boundedness on the local Hardy space…

Let $\varphi: {\mathbb R^n}\times [0,\infty)\to[0,\infty)$ be such that $\vz(x,\cdot)$ is nondecreasing, $\varphi(x,0)=0$, $\varphi(x,t)>0$ when $t>0$, $\lim_{t\to\infty}\varphi(x,t)=\infty$ and $\vz(\cdot,t)$ is a Muckenhoupt…

We consider maximal kernel-operators on abstract measure spaces $(X,\mu)$ equipped with a ball-basis. We prove that under certain asymptotic condition on the kernels those operators maps boundedly BMO(X) into BLO(X), generalizing the…

The uniformization and hyperbolization transformations formulated by Bonk, Heinonen and Koskela in \emph{"Uniformizing Gromov Hyperbolic Spaces"}, Ast\'erisque {\bf 270} (2001), dealt with geometric properties of metric spaces. In this…

Let $\L$ be a Schr\"odinger operator of the form $\L=-\Delta+V$ acting on $L^2(\mathbb R^n)$, $n\geq3$, where the nonnegative potential $V$ belongs to the reverse H\"older class $B_q$ for some $q\geq n.$ Let ${\rm BMO}_{{\mathcal{L}}}(\RR)$…

Let $(X,d,\mu)$ be a non-homogeneous metric measure space satisfying both the geometrically doubling and the upper doubling measure conditions. In this paper, the boundedness of multilinear fractional integral operator in this setting is…

Let $X$ be a ball quasi-Banach function space satisfying some minor assumptions. In this article, the authors establish the characterizations of $H_X(\mathbb{R}^n)$, the Hardy space associated with $X$, via the Littlewood--Paley…

We study the asymptotic behavior of three classes of nonlocal functionals in complete metric spaces equipped with a doubling measure and supporting a Poincar\'e inequality. We show that the limits of these nonlocal functionals are…