一类全不连通群上的BMO和奇异积分算子

本文主要讨论了定义在局部紧的全不连通群Ｇ上的一类卷积算子在加权Ｌ^∞（Ｇ）和ＢＭＯ（ａ）空间的性态．证明了如果卷积算子的核满足适当的条件,则算子是Ｌ^∞（Ｇ）到ＢＭＯ（ａ）有界的或是ＢＭＯ（ａ）到ＢＭＯ（ａ）有界的．     

BMO与弱核条件下的Calderón-Zygmund算子交换子的有界性

本文证明了BMO与弱核条件下Calderón-Zygmund奇异积分算子的交换子 [B,T]f=BTf-T(Bf)的L2有界性,这里B ∈BMO,T对增生的b1,b2,满足 T(b1)∈BMO,T*(b2)∈BMO,b2Tb1∈WBP．     

Real interpolation between martingale hardy and BMO spaces

In this paper, we consider the real interpolation with a function parameter between martingale Hardy and BMO spaces. An interpolation theorem for martingale Hardy and BMO spaces is formulated. As an application, real interpolation between martingale Lorentz and BMO spaces is given.     

BMO from dyadic BMO on the bidisc

We generalize to the bidisc a theorem of Garnett and Jones relatingthe space BMO of functions of bounded mean oscillation to itsmartingale counterpart, dyadic BMO. Namely, translation-averagesof suitable families of dyadic BMO functions belong to BMO.As a corollary, we deduce a biparameter version of a theoremof Burgess Davis connecting the Hardy space H¹ to martingaleH¹. We also prove the analogs of the theorem of Garnett andJones in the one-parameter and biparameter VMO spaces of functionsof vanishing mean oscillation.     

广义Littlewood-Paley函数的BMO有界性

本文证明了BMO函数在广义Littlewood-Paley函数下的象或者几乎处处等于无穷或者属于BMO。     

BMO Spaces and John-Nirenberg Estimates for the Heisenberg Group Targets

In this paper, the BMO spaces for the Heisenberg group targets are studied. Some properties of the BMO spaces and the John-Nirenberg estimates are obtained.     

具有BMO系数的拟线性椭圆方程解的BMO估计

We establish a global limiting case of nonlinear Calderon-Zygmund theory to quasilinear elliptic equations div A(x,Du) = div(|F|~(p-2)F) under the BMO smallness of the nonlinearity,that is |F|~(p-2)F∈BMO implies that Du ∈BMO.     

齐型空间上$L^1$ 与{\rm BMO}的内插空间

本文讨论齐型空间上$L^1$ 与{\rm BMO}的内插空间, 得到下列结果:对于本文讨论齐型空间上$L^1$ 与{\rm BMO}的内插空间, 得到下列结果:对于本文讨论齐型空间上$L^1$ 与{\rm BMO}的内插空间, 得到下列结果:对于摘要：本文讨论齐型空间上L^1与BMO的内插空间，得到下列结果：对于0〈θ〈1，1≤q≤∞，有（L^1，BMO）θ，q=Lpq，其中θ=1-1/p。     

Some new characterizations on spaces of functions with bounded mean oscillation

Let X be a space of homogeneous type. The authors introduce some generalized approximations to the identity (for short, GAI) with optimal decay conditions in the sense that these conditions are the sufficient and necessary conditions for these GAI's to characterize BMO(X), the space of functions with bounded mean oscillation on X. The authors also obtain a new John‐Nirenberg‐type inequality associated with GAI's, which leads some new characterizations of BMO(X) in terms of rearrangement functions, and certain maximal functions related to GAI's. Some variants of these characterizations for BMO‐type spaces on X of Duong and Yan are also established. Moreover, the equivalence between BMO and the space of BMO type on Ahlfors n ‐regular quasimetric measure spaces is obtained, which confirms an assertion of Duong and Yan (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

新的齐型BMO, Lipschitz空间上的奇异积分算子

Let(X, d, μ) be a space of homogeneous type, BMO_A(X) and Lip_A(β,X) be the space of BMO type,lipschitz type associated with an approximation to the identity {A_t}_t0 and introduced by Duong,Yan and Tang, respectively. Assuming that T is a bounded linear operator on L~2(X), we find the sufficient condition on the kernel of T so that T is bounded from BMO(X) to BMO_A(X) and from Lip(β, X) to Lip_A(β, X). As an application, the boundedness of Calderón-Zygmund operators with nonsmooth kernels on BMO(R~n) and Lip(β, R~n) are also obtained.     

Characterizations of bounded mean oscillation on the polydisk in terms of Hankel operators and Carleson measures

A scale of BMO spaces appears naturally in product spaces corresponding to the different, yet equivalent, characterizations of the class of functions of bounded mean oscillation in one variable. S.-Y. Chang and R. Fefferman characterized product BMO, the dual of the (real) Hardy spaceH _Re ¹ on product domains, in terms of Carleson measures. Here we describe two other BMO spaces, one contained in and the other containing product BMO, in terms of Carleson measures and Hankel operators. Both of these spaces play a significant role in harmonic analysis of the polydisk and in multivariable operator theory. First author supported in part by a grant from the National Science Foundation. Second author supported in part by a grant from the Department of Energy.     

关于参数型Marcinkiewicz积分的BMO有界性

本文研究了BMO空间上参数型Marcinkiewicz积分的有界性.利用Marcinkiewicz积分及BMO空间的性质,得到了该积分算了在BMO空间上是有界的.     

New Proofs of Some Results on Bounded Mean Oscillation Martingales Using Backward Stochastic Differential Equations

Using properties of backward stochastic differential equations, we give new proofs of some well-known results on bounded mean oscillation (BMO) martingales and improve some estimates of BMO norms.     

高维分数次Hardy算子交换子的λ中心BMO估计

本文得到了高维Hardy算子在λ中心BMO空间上有界的最佳常数,并建立了高维分数次Hardy算子交换子在中心Morrey空间上的λ中心BMO估计.     

加权变指标Herz-Morrey空间上的双线性Hardy算子的交换子

本文利用权范数给出BMO函数的一个新刻画.作为此刻画的一个应用,获得了双线性Hardy算子和BMO函数生成的交换子在加权变指标Herz-Morrey乘积空间上的有界性.     

Vector-valued Inequalities for Commutators of Singular Integrals on Herz Spaces with Variable Exponents

Based on the theory of variable exponents and BMO norms,we prove the vector-valued inequalities for commutators of singular integrals on both homogeneous and inhomogeneons Herz spaces where the two main indices are variable exponents.Furthermore,we show that a wide class of commutators generated by BMO functions and sublinear operators satisfy vector-valued inequalities.     

A Precise Interplay Between BMO Space and A 2 Class in Dimension One

Sharp inequalities between weight bounds from A ₂-condition and the BMO norm or the distance from L ^∞ in the BMO norm are obtained in the one dimensional case.     

POINTWISE MULTIPLIERS FOR LOCALIZED MORREY-CAMPANATO SPACES ON RD-SPACES

In this article, the authors characterize pointwise multipliers for localized MorreyCampanato spaces, associated with some admissible functions on RD-spaces, which include localized BMO spaces as a special case. The results obtained are applied to Schrdinger operators and some Laguerre operators.     

Bmo boundedness for banach space valued singular integrals

In this paper, we consider a class of Banach space valued singular integrals. The Lp boundedness of these operators has already been obtained. We shall discuss their boundedness from BMO to BMO. As applications, we get BMO boundednessfor the classic g-function and the Marcinkiewicz integral. Some known results are improved.