Weighted Composition Followed and Proceeded by Differentiation Operators from Q_k(p,q) Space to Weighted α-Bloch Space

We study the boundedness and compactness of the weighted composition followed and proceeded by differentiation operators from Q_k（p,q）space to weighted α-Bloch space and little weighted α-Bloch space.Some necessary and sufficient conditions for the boundedness and compactness of these operators are given.

PRODUCT TYPE OPERATORS ACTING BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES

For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.

TOEPLITZ OPERATORS BETWEEN WEIGHTED BERGMAN SPACES OVER THE HALF-PLANE

In this paper,by characterizing Carleson measures,we investigate a class of bounded Toeplitz operator between weighted Bergman spaces with Békolléweights over the half-plane for all index choices.

MULTIPLICATION OPERATORS ON WEIGHTED DIRICHLET SPACES

In this paper,we study multiplication operators on weighted Dirichlet spaces D_(β)(β∈R).Let n be a positive integer and β∈R,we show that the multiplication operator M_(z)^(n) on D_(β) is similar to the operator ⊕_(1)^(n)M_(z)on the space⊕_(1)^(n)D_(β).Moreover,we prove that M_(z)^(n)(≥2)on Dβis unitarily equivalent to ⊕_(1)^(n)M_(z) on⊕_(1)^(n)D_(β) if and only if β=0.In addition,we completely characterize the unitary equivalence of the restrictions of M_(z)^(n) to different invariant subspaces z^(k)D_(β)(k≥1),and the unitary equivalence of the restrictions of M_(z)^(n) to different invariant subspaces S_(j)(0≤j<n).Abkar,Cao and Zhu[Complex Anal Oper Theory,2020,14:Art 58]pointed out that it is an important,natural,and difficult question in operator theory to identify the commutant of a bounded linear operator.They characterized the commutant A′( M_(z)^(n))of M_(z)^(n)on a family of analytic function spaces A_(α)^(2)(α∈R)on D(in fact,the family of spaces A_(α)^(2)(α∈R)is the same with the family of spaces D_(β)(β∈R))in terms of the multiplier algebra of the underlying function spaces.In this paper,we give a new characterization of the commutant A′( M_(z)^(n))of M_(z)^(n)on D_(β),and characterize the self-adjoint operators and unitary operators in A'(M_(z)^(n)).We find that the class of self-adjoint operators(unitary operators)in A'(M_(z)^(n))when β≠0 is different from the class of self-adjoint operators(unitary operators)in A′( M_(z)^(n))when β=0.

Weighted multilinear p-adic Hardy operators and commutators on p-adic Herz-type spaces

In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given.

THE BOUNDEDNESS OF OPERATORS ON WEIGHTED MULTI-PARAMETER LOCAL HARDY SPACES

Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.

Weighted Composition Operators fromα-Bloch Spaces to H~∞

The article not only presents the boundedness and compactness of the weighted composition operator from α-Bloch spaces（or little α-Bloch spaces） to H^∞, but also gives some estimates for the norm of the weighted composition operator.

The Interpolation of Operators between Weighted Hardy Spaces and Weighted L^p Spaces

The paper is given the interpolation of operators between weighted Hardy spaces and weighted L p spaces when w∈A 1 by Calderon Zygmund decomposition.

On Weighted Tent Space

In this paper, we introduce the A, weights into the tent space, many important results in the tent space are generalized. Also, new relations between the A, weights and Carleson measures are obtained.

MRI相位导航技术下2D T2-TSE与3D T2-SPACE序列在疑似隐匿性脊髓栓系综合征俯卧位扫描中的应用价值对比

目的对比MRI相位导航技术下二维T2加权快速自旋回波(two dimensional T2 weighted imaging turbo spin echo,2D T2-TSE)序列与三维T2加权可变翻转角快速自旋回波(three dimensional T2 weighted imaging sampling perfection with application optimized contrast using different flip angle evolution,3D T2-SPACE)序列在疑似隐匿性脊髓栓系综合征(occult tethered cord syndrome,OTCS)俯卧位扫描中的图像质量和临床应用价值。材料与方法回顾性分析2023年1月至2023年10月在我院接受MRI检查的疑似OTCS的6岁以下患者30例,均采用相位导航技术下俯卧位2D T2-TSE和3D T2-SPACE序列进行检查。根据所得图像整体质量、脊髓圆锥显示、马尾神经及终丝显示、蛛网膜下腔脑脊液信号显示、背景噪声显示情况进行主观评分,记录扫描时间,计算椎管内的图像信噪比(signal-to-noise ratio,SNR)和对比噪声比(contrast-to-noise ratio,CNR)。比较两种序列的图像质量的主观评分、扫描时间、椎管内SNR与CNR的客观分析。分别采用配对t检验、Mann-Whitney U检验,将两种检查方法的评估结果进行对比分析。通过Kappa检验分别评估两名医师主观评分的一致性,以及两名技师客观定量分析的一致性。结果图像质量的主观评分中,两名医师的评分一致性较强(Kappa=0.794,P<0.001),3D T2-SPACE序列图像整体质量、马尾神经及终丝显示、蛛网膜下腔脑脊液信号显示以及背景噪声显示评分均高于2D T2-TSE序列(Z=-2.305、-4.242、-3.453、-2.201,P均<0.05),在脊髓圆锥显示上,2D T2-TSE与3D T2-SPACE序列一致(Z=-0.948,P>0.05)。客观定量分析中,两名技师对椎管内SNR与CNR测量结果的一致性很强(Kappa=0.851、0.734,P均<0.001),2D T2-TSE对比3D T2-SPACE序列,两次测量的数据分析结果中3D T2-SPACE序列椎管内SNR和CNR均优于2D T2-TSE序列(第一次测量SNR与CNR:t=-3.058、-3.703;第二次测量SNR与CNR:t=-2.981、-2.965,P均<0.05)。3D T2-SPACE序列扫描时间较2D T2-TSE序列扫描时间长[(183.67±34.89)s vs.(120.53±27.93)s,t=-10.087,P<0.001]。结论在疑似OTCS患者的俯卧位MRI检查中,相位导航技术下的3D T2-SPACE序列相比2D T2-TSE序列可以提供更优良的椎管内图像质量、更小的FOV与体素,为临床诊治提供更多可靠信息。

INTERIOR ESTIMATES IN MORREY SPACES FOR SOLUTIONS OF ELLIPTIC EQUATIONS AND WEIGHTED BOUNDEDNESS FOR COMMUTATORS OF SINGULAR INTEGRAL OPERATORS

It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp, (w).

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.

WEIGHTED COMPOSITION OPERATORS BETWEEN DIRICHLET SPACES

In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are different counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.

The Boundedness of Littlewood-Paley Operators with Rough Kernels on Weighted (L^q , L^p )~α (R^n) Spaces

In this paper, we shall deal with the boundedness of the Littlewood-Paley operators with rough kernel. We prove the boundedness of the Lusin-area integral μΩs and Littlewood-Paley functions μΩ and μλ^＊ on the weighted amalgam spaces （Lω^q,L^p）^α（R^n）as 1〈q≤α〈p≤∞.

ESSENTIAL NORMS OF PRODUCTS OF WEIGHTED COMPOSITION OPERATORS AND DIFFERENTIATION OPERATORS BETWEEN BANACH SPACES OF ANALYTIC FUNCTIONS

We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.

CONVERGENCE OF WEIGHTED AVERAGES OF MARTINGALES IN NONCOMMUTATIVE BANACH FUNCTION SPACES

Let x （xn）≥1 be a martingale on a noncommutative probability space n （M, r） and （wn）n≥1 a sequence of positive numbers such that Wn = ∑ k=1^n wk →∞ as n →∞ We prove that x = （x.）n≥1 converges in E（M） if and only if （σn（x）n≥1 converges in E（.hd）, where E（A//） is a noncommutative rearrangement invariant Banach function space with the Fatou property and σn（x） is given by σn（x） = 1/Wn ∑k=1^n wkxk, n=1, 2, .If in addition, E（Ad） has absolutely continuous norm, then, （an（x））≥1 converges in E（.M） if and only if x = （Xn）n≥1 is uniformly integrable and its limit in measure topology x∞∈ E（M）.

WEIGHTED COMPOSITION OPERATORS ON WEIGHTED DIRICHLET SPACES

We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.

MULTIPLIERS AND RELATIVE COMPLETION IN WEIGHTED LORENTZ SPACES

Let G be a locally compact Abelian group with Haar measure μ. In the present paper, first the authors discussed some properties of weighted Lorentz space. Then they defined the relative completion A of a subspace A of the weighted Lorentz space, and showed that the space of the multipliers from L_w~1,(G) to A is algebrically isomorphic and homeomorphic to A.

Boundedness of Hausdorff operators on the power weighted Hardy spaces

In this paper, we consider the two-dimensional Hausdorff operators on the power weighted Hardy space H;（R;） （ -1 ≤α≤0）, defined by H;f（x）=∫R;Φ（u）f(A（u）x)du,where Φ∈L;oc;（R;）,A（u） = (α;（u）);is a 2×2 matrix, and each α;is a measurablefunction.We obtain that HΦ,A is bounded from H;（R;） （ -1≤α≤0） to itself, if∫R2|Φ（u）‖det A;（u）|‖A（u）‖;ln(1+‖A;（u）‖;/|det A;（u）|)du<∞.This result improves some known theorems, and in some sense it is sharp.

DUALITY OF WEIGHTED MULTIPARAMETER TRIEBEL-LIZORKIN SPACES

In this paper, we reintroduce the weighted multi-parameter Triebel-Lizorkin spaces Fp^a,q（w;R^n1×R^n2） based on the Frazier and Jawerth＇ method in [11]. This space was firstly introduced in [18]. Then we establish its dual space and get that （Fp＇q）＊ = CMOp^-a,q＇ for 0 ~p≤ 1.