齐型空间上极大奇异积分算子的有界性估计

借助函数分解、空间分解的技巧,利用重整函数的不等式性质,得到极大奇异积分算子T的关于p是线性级的LP(X,ω(x)dμ)有界性估计:     

Weighted Boundedness for Generalized Maximal andSingular Integral Operators in Orlicz-Morrey Spaces

51.IntroductionTheweightedboundednessformaximalandsingularintegraloperatorsonLp(p>1)andBMofunctionspacesarenowunderstood(see[lj)-AsMorreyspacemaybeconsideredasanextensionofthespaces,itisnaturalandimportanttostudytheweightedbou11dednessformax-imalandsingularintegraloperatorsonMorreyspaces.Thepurposeofthispaperistostu`lythequestion,theweightedboundednessfortheoperatorsinOrlicz-Morreyspacesareobtained,andthecharacterizationsfornon-weightedboundednessofmaximaloperatorarealsoobtained.Someworkint…     

齐型空间上极大交换子的一个加权估计

本文建立齐型空间上与奇异积分算子和BMO构成的交换子相应的极大算子的一个带一般权的加权L~p估计.     

奇异积分交换子的加权Hardy型估计

T_b表示由加权Lipschitz函数b∈Lip_β(μ)(0β1)与Calderon-Zygmund奇异积分算子T生成的交换子.当μ∈A_1,n/(n+β)p≤1时研究了T_b在经典加权Hardy空间H~p(μ))上的有界性质,在端点p=n/(n+β)处研究了T_b在加权Hardy空间上的弱型估计.     

极大算子的加权BLO估计(英文)

引入加权BLO空间,得到了极大奇异积分算子和Hardy-Littlewood极大算子的加权BLO估计.     

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.     

Toeplitz Type Operator Associated to Singular Integral Operator with Variable Kernel on Weighted Morrey Spaces

Suppose Tk,1 and Tk,2 are singular integrals with variable kernels and mixed homogeneity or ± I(the identity operator). Denote the Toeplitz type operator by Tb=∑Qk=1Tk,1MbTk,2,where Mbf=bf. In this paper, the boundedness of Tbon weighted Morrey space are obtained when b belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.     

一类奇异积分算子在加权空间的界的估计

设T是由Grubb和Moore引入的一类奇异积分算子,它的核满足一种新型利普希茨正则性.T*是由T确定的极大奇异积分算子.本文通过建立与T和T*相关的grand极大算子的弱型端点估计,得到了算子T和T*在加权空间的由Ap权常数表示的界的估计和弱型端点估计.     

Boundedness of Rough Singular Integral Operators on Homogeneous Herz Spaces with Variable Exponents

We establish the boundedness of rough singular integral operators on homogeneous Herz spaces with variable exponents. As an application, we obtain the boundedness of related commutators with BMO functions on homogeneous Herz spaces with variable exponents.     

Weighted Lp Estimates for Maximal Commutators of Multilinear Singular Integrals

This paper is concerned with the pointwise estimates for the sharp function of two kinds of maximal commutators of multilinear singular integral operators T∑b^＊ and TПb^＊ which are generalized by a weighted BMO function b and a multilinear singular integral operator T, respectively. As applications, some commutator theorems are established.     

齐次Morrey-Herz空间中交换子的中心BMO估计

设T_b为广义Hardy算子和中心BMO函数生成的交换子,本文得到了该交换子在齐次加权Morrey-Herz空间中的有界性.而且,本文给出了带粗糙核的多线形奇异积分算子在齐次Morrey-Herz空间中的中心BMO估计.     

与分数次积分和具有非光滑的奇异积分算子相关的Toeplitz型算子在Morrey空间的有界性

本文证明了与分数次积分和具有非光滑的奇异积分算子相关的Toeplitz型算子的sharp极大函数估计,做为应用,得到了该算子在Morrey空间的有界性.     

奇异积分交换子在加权Herz型Hardy空间上的有界性质

T_b表示由加权Lipschitz函数b与Calderon-Zygmund奇异积分算子T生成的交换子.研究了T_b在加权Herz型Hardy空间上的有界性质,并在端点处证明了交换子是从加权Herz型Hardy空间到加权弱Herz空间的有界算子.     

非齐型空间上分数型Marcinkiewicz积分算子的加权估计

令（X,d,μ）为满足所谓上倍双倍条件和几何双倍条件的度量测度空间.设M_β,ρ,q为（X,d,μ）上的分数型Marcinkiewicz积分算子.在本文中,作者证明了若β ∈[0,∞）,ρ ∈（0,∞）,q ∈（1,∞）且M_β,ρ,q在L²（μ）上有界,则M_β,ρ,q是从加权Lebesgue空间L^p（w）到加权弱Lebesgue空间L^p,∞（w）上有界和从加权Morrey空间L^p,κ,η（ω）到加权弱Morrey空间WL^p,κ,η（ω）上有界.     

分数次积分算子的交换子在齐型空间上的弱型估计

本文研究分数次积分交换子,其中Kα(x,y)=d(x,y)α-1,m∈N且b(x)∈BMO(X,μ),证明了Iα,bm是从Orlicz空间L(log L)m(X)到弱Lq(X)空间的映照．同时还证明了分数次极大算子交换子Mα,bm也有类似性质．     

极大奇异积分算子的一个BLO估计

本文研究以(Ω(x)/|z|n))为核的极大齐次奇异积分算子在空间BMO(R~n)上的性质,其中Ω是一个零阶齐次函数且在单位球面上均值为零．可以证明：若Ω满足某种最小尺度条件和某种L~1-Dini型正则性条件,则此极大奇异积分算子是由BMO(R~n)到BLO(R~n)的有界算子．     

齐型空间中分数次积分交换子的加权端点估计

该文得到齐型空间中分数次积分交换子[b,I_α]的加权端点估计ω({x∈X:|[b,I_α]f(x)|t})≤Cψ(∫_xA(||b||_*(|f(x)|/t)■(ω(x))dμ(x))其中b∈BMO(X,d,μ),A(t)=tlog(e+t),ψ(t)=[tlog(e+t~α)]~(1/(1-α)),■(t)=t~(1-α)log(e+t~(-α)).     

与一类奇异积分算子相关的Toeplitz型算子的有界性

对与具有一般核的分数次奇异积分算子相关的Toeplitz型算子,本文证明了其sharp极大函数不等式,作为应用,得到了该算子在Lebesgue空间,Morrey空间和Triebel-Lizorkin空间的有界性.     

Littlewood-Paley g-函数交换子的加权估计

设g_(φ,b)是Littlewood-Paley g-函数与b生成的交换子,ω∈A_1.证明了若b属于加权BMO空间BMO(ω),则g_(φ,b)是L~p(ω)到L~p(ω~(1-p))(1p∞)有界的;若b属于加权Lipschitz空间Lip_β(ω)(0β1),则g_(φ,b)是L~p(ω)到L~q(ω~(1-q))的有界算子,其中1pq∞,1/q=1/p-β/n.