THE CENTRAL BMO SPACES AND LITTLEWOOD-PALEY OPERATORS

The authors give a characterization of central bounded mean oscillation space CBMO2(Rγ) in terms of the central Carleson measure. Using this character, the authors establish the CBMO2(Rγ)-boundedness for several classes of general Littlewood-Paley operators.

Two New BMO Spaces and Sharp Operators of B-Valued Martingale

For Banach space-valued martingale, two new BMO spaces, namely BMO (X), resp-BMO (X), and two new sharp operators, namely, resp. generated by the condition-al p-mean-square resp. p-mean-square operator are introduced, and then, the connections betweenBMO (X) and BMO;, BMO(X) and BMO and and are investigated. The resultsobtained here yield a new charactrization of the convexity and smoothness of Banach space.

EQUIVALENCES BETWEEN BLOCH TYPE SPACES AND BMO SPACES ON THE HYPERBOLIC DOmAINS IN C

For an analytic function f on the hyperbolic domain Ω in C,the following conclusions are obtained: (i)f∈B(Ω)=BMOA(Ω,m)if and only if Ref∈B(?)(Ω)=BMOH(Ω,m).(ii)QB_h(Ω)=B_h(Ω) (BMOH,(Ω,m)=BMOH(Ω,m)if and only if C(Ω)=inf{Z_o(z)·δ_o(z)·z≡Ω}>0,Also some applica- lions to automorphic function are considered.

On the Blow-up Criterion of Smooth Solutions to the MHD System in BMO Space

In this paper we study the blow-up criterion of smooth solutions to the incompressible magnetohydrodynamics system in BMO space. Let （u（x,t）,b（x,t）） be smooth solutions in （0, T）. It is shown that the solution （u（x, t）, b（x, t）） can be extended beyond t = T if （u（x,t）, b（x, t）） ∈ L^1 （0, T; BMO） or the vorticity （rot u（x, t）, rot b（x, t）） ∈ L^1 （0, T; BMO） or the deformation （Def u（x, t）, Def b（x, t）） ∈ L^1 （0, T; BMO）.

A characterization of λ-central BMO space

We give a characterization of the λ-central BMO space via the boundedness of commutators of n-dimensional Hardy operators.

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. Keywords Martingale space, BMO space, Lorentz space, real interpolation, function parameter

Characterizations of Weighted BMO Space and Its Application

In this paper,we prove that the weighted BMO space BMO^(p)(ω)={f∈L^(1)_(loc):sup||χQ||^(-1)Lp(ω)||(F-Fq)ω^(-1)χQ||LP(ω)<∞Q}is independent of the scale p∈(0,∞)in sense of norm whenω∈A_(1).Moreover,we can replace L^(p)(ω)by L^(p,∞)(ω).As an application,we characterize this space by the boundedness of the bilinear commutators[b,T]_(j)(j=1,2),generated by the bilinear convolution type Calderdn-Zygmund operators and the symbol b,from L^(p1)(ω)×L^(p2)(ω)to L^(p)(ω^(1-p))with 1<p1,p2<∞and 1/p=1/p1+1/p2.Thus we answer the open problem proposed by Chaffee affirmatively.

THE FRACTIONAL TYPE MARCINKIEWICZ INTEGRALS AND COMMUTATORS ON WEIGHTED HARDY SPACES

This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of that the homogeneous kernelΩsatisfies certain regularities,the authors obtain the boundedness ofμΩ,βfrom the weighted Hardy spaces Hωpp(Rn)to the weighted Lebesgue spaces Lωqq(Rn)for n/(n+β)≤<p≤1 with 1/q=1/p-β/n,as well as the same(Hωpp,Lωqq)-boudedness ofμΩ,βb when b belongs to BMOωp,p(Rn),which is a non-trivial subspace of BMO(Rn).

Carleson measures, BMO spaces and balayages associated to Schrdinger operators

Let L be a Schrdinger operator of the form L =-? + V acting on L^2(R^n), n≥3, where the nonnegative potential V belongs to the reverse Hlder class B_q for some q≥n. Let BMO_L(R^n) denote the BMO space associated to the Schrdinger operator L on R^n. In this article, we show that for every f ∈ BMO_L(R^n) with compact support, then there exist g ∈ L~∞(R^n) and a finite Carleson measure μ such that f(x) = g(x) + S_(μ,P)(x) with ∥g∥∞ + |||μ|||c≤ C∥f∥BMO_L(R^n), where S_(μ,P)=∫(R_+^(n+1))Pt(x,y)dμ(y, t),and Pt(x, y) is the kernel of the Poisson semigroup {e-^(t(L)^(1/2))}t>0 on L^2(R^n). Conversely, if μ is a Carleson measure, then S_(μ,P) belongs to the space BMO_L(R^n). This extends the result for the classical John-Nirenberg BMO space by Carleson(1976)(see also Garnett and Jones(1982), Uchiyama(1980) and Wilson(1988)) to the BMO setting associated to Schrdinger 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 boundedness for the classic g-function and the Marcinkiewicz integral. Some known results are improved.

COMMUTATORS OF BMO FUNCTIONS AND SINGULAR INTEGRAL OPERATORS WITH NON-SMOOTH KERNELS ON SPACES OF HOMOGENEOUS TYPE OF FINITE MEASURE

让 X 是有有限措施的同类的类型的一个空格。让 T 是在 L^p (X) 上被围住的一个单个不可分的操作员， 1 【 p 【 ∞。我们在核 k 上给一个足够的条件( x ， y ) T 以便什么时候功能 b ∈ BMO (X)，整流器[ b ， T ](f)= T ( bf )- bT (f)为所有 p 在空格 L^p 上被围住， 1 【 p 【 ∞。

伴随BMO函数的交换子在Herz型Hardy空间上的加权有界性

记 [b ,T]为由BMO函数b与广义Calder幃ｎ Zygmund算子T生成的交换子 .研究了 [b ,T]在Herz型Hardy空间上的有界性及其加权有界性 .

BOUNDEDNESS OF FRACTIONAL MAXIMAL OPERATOR AND THEIR HIGHER ORDER COMMUTATORS IN GENERALIZED MORREY SPACES ON CARNOT GROUPS

In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G （i.e., nilpotent stratified Lie group） in the generalized Morrey spaces Mp,φ（G）, where Q is the homogeneous dimension of G. We find the conditions on the pair （φ1, φ2） which ensures the boundedness of the operator Ms from one generalized Morrey space Mp,φ1 （G） to another Mq,φ2 （G）, 1. 〈 p ≤q 〈 ∞. 1/p - 1/q = α/Q, and from the space M1,φ1 （G） to the weak space Wq,φ2 （G）, 1 〈 q 〈 ∞, 1 - 1/q = α/Q. Also find conditions on the φ which ensure the Adams type boundedness of the Ms from M α （G） from Mp,φ^1/p（G）to Mq,φ^1/q（G） for 1 〈p〈q〈∞ and fromM1,φ（G） toWMq,φ^1/q（G）for 1〈q〈∞. In the case b ∈ BMO（G） and 1 〈 p 〈 q 〈 ∞, find the sufficient conditions on the pair （φ1, φ2） which ensures the boundedness of the kth-order commutator operator Mb,α,k from Mp,φ1 （G） to Mq,φ2（G） with 1/p - 1/q = α/Q. Also find the sufficient conditions on the φ which ensures the boundedness of the operator Mb,α,k from Mp,φ^1/p（G） tom Mp,φ^1/p （G） for 1 〈p〈q〈∞. In all the cases the conditions for the boundedness of Mα are given it terms of supremaltype inequalities on （φ1, φ2） and φ , which do not assume any assumption on monotonicity of （φ1, φ2） and φ in r. As applications we consider the SchrSdinger operator -△G ＋ V on G, where the nonnegative potential V belongs to the reverse Holder class B∞（G）. The MB,φ1 - Mq,φ2 estimates for the operators V^γ（-△G ＋ V）^-β and V^γ△↓G（-△G ＋ V）^-β are obtained.

Weighted boundedness of some integral operators on weighted λ-central Morrey space

In this paper, the authors prove the weighted boundedness of singular integral and fractional integral with a rough kernel on the weighted λ-central Morrey space. Moreover, the weighted estimate for commutators of singular integral with a rough kernel on the weighted λ-central Morrey space is also given.

ANALYTIC HARDY SPACES ON THE QUANTUM TORUS

Analytic Hardy and BMO spaces on the quantum torus are introduced. Some basic properties of these spaces are presented. In particular, the associated H 1-BMO duality theorem is proved. Finally, we discuss some possible extensions of the obtained results.

λ-central BMO Estimates for Higher Order Commutators of Hardy Operators

In this paper, the λ-central BMO estimates for higher order commuta-tors of Hardy operators on central Morrey space Lq,λ（Rn） are established. In the meanwhile, the corresponding corollary for central BMO estimates is also obtained.

BOUNDS FOR MULTILINEAR OPERATORS UNDER AN INTEGRAL TYPE CONDITION ON MORREY SPACES

In this paper,we study a boundedness property of the Adams type for multilinear fractional integral operators with the multilinear L^(r′,α)-Hörmander condition and their commutators with vector valued BMO functions on a Morrey space and a predual Morrey space.Moreover,we give an endpoint estimate for multilinear fractional integral operators.As an application,we obtain the boundedness of multilinear Fourier multipliers with limited Sobolev regularity on a Morrey space.

有界对称域上的BMO^p空间的乘子

该文得到在 Bergman度量下刻划有界 p-次平均振动函数 (BMOp)空间的乘子的几个等价条件 ,包含了文献 [3]中的

一类与高阶Schrödinger型算子相关的变分算子的BMO交换子有界性

设L=(-Δ)^(2)+V^(2)是R^(n)(n≥5)上的高阶Schrödinger型算子,其中非负位势V属于反向Hölder类RHq(q>n/2).记Vp(e^(-tL)),为与高阶Schrödinger型算子L相关的变分算子.基于Herz型Hardy空间的原子分解理论,利用Schrödinger型算子的性质,证明了这类变分算子与BMO函数构成的交换子是从HerzHardy空间到Herz空间有界的,也是在Morrey-Herz空间上有界的结果.