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.

WEIGHTED NORM INEQUALITIES FOR THE COMMUTATORS OF MULTILINEAR SINGULAR INTEGRAL OPERATORS

In this paper, the authors consider the weighted estimates for the commutators of multilinear Calderón-Zygmund operators.By introducing an operator which shifts the commutation, and establishing the weighted estimates for this new operator, the authors prove that, if p_1 ∈ （1,∞）, p_2,…,p_m ∈（1,∞], p ∈ （0,∞） with 1/p =Σ1≤k≤ m 1/pk, then for any weight w, the commutators of m-linear Galderón-Zygmund operator are bounded from L P1（R n,M_l（logL） σw）× p2（Rn,M~w）×...×Lpm（Rn,Mw） to Lp（Rn,w）with σ to be a constant depending only on p_1 and the order of commutator

WEIGHTED INEQUALITIES AND APPLICATIONS TO BEST LOCAL APPROXIMATION IN LUXEMBURG NORM

In this paper we establish a result about uniformly equivalent norms and the convergence of best approximant pairs on the unitary ball for a family of weighted Luxemburg norms with normalized weight functions depending on ε, when ε→ 0. It is introduced a general concept of Pade approximant and we study its relation with the best local quasi-rational approximant. We characterize the limit of the error for polynomial approximation. We also obtain a new condition over a weight function in order to obtain inequalities in Lp norm, which play an important role in problems of weighted best local Lp approximation in several variables.

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.

SAR image de-noising based on texture strength and weighted nuclear norm minimization

As synthetic aperture radar（SAR） has been widely used nearly in every field, SAR image de-noising became a very important research field. A new SAR image de-noising method based on texture strength and weighted nuclear norm minimization（WNNM） is proposed. To implement blind de-noising, the accurate estimation of noise variance is very important. So far, it is still a challenge to estimate SAR image noise level accurately because of the rich texture. Principal component analysis（PCA） and the low rank patches selected by image texture strength are used to estimate the noise level. With the help of noise level, WNNM can be expected to SAR image de-noising. Experimental results show that the proposed method outperforms many excellent de-noising algorithms such as Bayes least squares-Gaussian scale mixtures（BLS-GSM） method, non-local means（NLM） filtering in terms of both quantitative measure and visual perception quality.

AN INTERACTIVE METHOD FOR THE MULTIOBJECTIVE DECISION BASED ON THE WEIGHTED TCHEBYCHEFF NORM

In this paper, we propose an interactive method for the multiobjec-tive decision making problem. It can produce a quality solution of a decision mak-er(DM) by using the Tchebycheff norm. At each interactive step, it only requiresthe DM make some index spe

AN UPPER BOUND OF THE ESSENTIAL NORM OF COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES

In this paper, we define the generalized counting functions in the higher dimensional case and give an upper bound of the essential norms of composition operators between the weighted Bergman spaces on the unit ball in terms of these counting functions. The sufficient condition for such operators to be bounded or compact is also given.

A WEIGHTED NORM INEQUALITY FOR THETA(t)-TYPE OSCILLATORY SINGULAR INTEGRALS

The theta (t)-type oscillatory singular integral operators has been discussed. With the non-negative locally integrable weighted function, the weighted norm inequality of theta ( t) -type oscillatory singular integral operators is proved, and the weighted function has replaced by action of Hardy-Littlewood maximal operators several times.

Weighted Nuclear Norm Minimization-Based Regularization Method for Image Restoration

Regularization methods have been substantially applied in image restoration due to the ill-posedness of the image restoration problem.Different assumptions or priors on images are applied in the construction of image regularization methods.In recent years,matrix low-rank approximation has been successfully introduced in the image denoising problem and significant denoising effects have been achieved.Low-rank matrix minimization is an NP-hard problem and it is often replaced with the matrix’s weighted nuclear norm minimization(WNNM).The assumption that an image contains an extensive amount of self-similarity is the basis for the construction of the matrix low-rank approximation-based image denoising method.In this paper,we develop a model for image restoration using the sum of block matching matrices’weighted nuclear norm to be the regularization term in the cost function.An alternating iterative algorithm is designed to solve the proposed model and the convergence analyses of the algorithm are also presented.Numerical experiments show that the proposed method can recover the images much better than the existing regularization methods in terms of both recovered quantities and visual qualities.

SEVERAL WEAK-TYPE WEIGHTED INEQUALITIES IN ORLICZ MARTINGALE CLASSES

The aim of this paper is to establish several necessary and sufficient conditions in order that the weighted inequality ρ（M f 〉 λ）Φ（λ） ≤ C ∫_Ω~Ψ （C｜f｜）σdμ,λ 〉 0 or ρ（Mf〉λ） ≤ C∫-Ω~Φ（Cλ^-1 ｜f｜）σdμ,λ 〉0 holds for every uniformly integral martingale f=（f_n）, where M is the Doob＇s maximal operator, Φ, Ψ are both Φ-functions, and e, σ are weights.

Application of Interpolation Inequalities to the Study of Operators with Linear Fractional Endpoint Singularities in Weighted Hölder Spaces

In this paper we consider operators with endpoint singularities generated by linear fractional Carleman shift in weighted Hölder spaces. Such operators play an important role in the study of algebras generated by the operators of singular integration and multiplication by function. For the considered operators, we obtained more precise relations between norms of integral operators with local singularities in weighted Lebesgue spaces and norms in weighted Hölder spaces, making use of previously obtained general results. We prove the boundedness of operators with linear fractional singularities.

Regularised Layerwise Weight Norm Based Skin Lesion Features Extraction and Classification

Melanoma is the most lethal malignant tumour,and its prevalence is increasing.Early detection and diagnosis of skin cancer can alert patients to manage precautions and dramatically improve the lives of people.Recently,deep learning has grown increasingly popular in the extraction and categorization of skin cancer features for effective prediction.A deep learning model learns and co-adapts representations and features from training data to the point where it fails to perform well on test data.As a result,overfitting and poor performance occur.To deal with this issue,we proposed a novel Consecutive Layerwise weight Con-straint MaxNorm model(CLCM-net)for constraining the norm of the weight vector that is scaled each time and bounding to a limit.This method uses deep convolutional neural networks and also custom layer-wise weight constraints that are set to the whole weight matrix directly to learn features efficiently.In this research,a detailed analysis of these weight norms is performed on two distinct datasets,International Skin Imaging Collaboration(ISIC)of 2018 and 2019,which are challenging for convolutional networks to handle.According to thefindings of this work,CLCM-net did a better job of raising the model’s performance by learning the features efficiently within the size limit of weights with appropriate weight constraint settings.The results proved that the proposed techniques achieved 94.42%accuracy on ISIC 2018,91.73%accuracy on ISIC 2019 datasets and 93%of accuracy on combined dataset.

Linear Combination of Derivative Weighted Composition Operators

The relation between composition operators on the Dirichlet spaces in the open unit disk and derivative weighted composition operators on the Bergman spaces in the open unit disk is investigated firstly,and for a combination of several derivative weighted composition operators which acts on classic Bergman space,the lower bound of its essential norm is estimated in terms of the boundary data of the symbols of d-composition operators.Some similar results about composition operators on the Dirichlet space are also presented.A necessary condition is given to determine the compactness of the combination of several derivative weighted composition operators on Bergman spaces.

Improved theory of generalized meteo-ballistic weighting factor functions and their use

It follows from the analysis of artillery fire errors that approximately two-thirds of the inaccuracy of indirect artillery fire is caused by inaccuracies in the determination of the meteo parameters included in fire error budget model.Trajectories calculated under non-standard conditions are considered to be perturbed.The tools utilized for the analysis of perturbed trajectories are weighting factor functions(WFFs)which are a special kind of sensitivity functions.WFFs are used for calculation of meteo ballistic elements B(ballistic wind w B,densityρB,virtual temperatureτB,pressure p B)as well.We have found that the existing theory of WFF calculation has several significant shortcomings.The aim of the article is to present a new,improved theory of generalized WFFs that eliminates the deficiencies found.Using this theory will improve methods for designing firing tables,fire control systems algorithms,and meteo message generation algorithms.

Frequency Weighting Filter Design for Automotive Ride Comfort Evaluation

Few study gives guidance to design weighting filters according to the frequency weighting factors,and the additional evaluation method of automotive ride comfort is not made good use of in some countries.Based on the regularities of the weighting factors,a method is proposed and the vertical and horizontal weighting filters are developed.The whole frequency range is divided several times into two parts with respective regularity.For each division,a parallel filter constituted by a low-and a high-pass filter with the same cutoff frequency and the quality factor is utilized to achieve section factors.The cascading of these parallel filters obtains entire factors.These filters own a high order.But,low order filters are preferred in some applications.The bilinear transformation method and the least P-norm optimal infinite impulse response（IIR） filter design method are employed to develop low order filters to approximate the weightings in the standard.In addition,with the window method,the linear phase finite impulse response（FIR） filter is designed to keep the signal from distorting and to obtain the staircase weighting.For the same case,the traditional method produces 0.330 7 m · s^–2 weighted root mean square（r.m.s.） acceleration and the filtering method gives 0.311 9 m · s^–2 r.m.s.The fourth order filter for approximation of vertical weighting obtains 0.313 9 m · s^–2 r.m.s.Crest factors of the acceleration signal weighted by the weighting filter and the fourth order filter are 3.002 7 and 3.011 1,respectively.This paper proposes several methods to design frequency weighting filters for automotive ride comfort evaluation,and these developed weighting filters are effective.

加权核范数最小化和改进小波阈值函数的图像去噪算法

针对加权核范数最小化算法存在结构残余噪声以及无法较好地保持图像边缘结构的问题,提出基于加权核范数最小化和改进小波阈值函数的图像去噪算法。利用全变分模型对噪声图像进行初步去噪,使用噪声图像与初步去噪后的图像进行差分运算,对差分后得到的噪声残差图像使用改进的小波阈值函数去噪,将小波去噪后的残差图像与初步去噪图像叠加,将叠加后的图像使用基于残余噪声水平迭代的加权核范数最小化算法进行二次去噪。相较于当下主流去噪算法,经该算法处理后的图像的PSNR和SSIM值均有所提升,能够更好地保持图像的纹理结构,且在高噪声环境下效果更佳。

张量学习诱导的多视图谱聚类

现有的方法将通过张量奇异值分解(t-SVD)正则化的低秩表示应用到多视图子空间聚类中,取得了令人印象深刻的聚类性能.然而,它们都具有以下两个共同的缺点:(1)他们专注于探索样本之间的关系以构建表征,然后将其堆叠为张量,其计算复杂度至少为O(n2logn);(2)他们总是直接在整合的表征上运行标准的谱聚类算法,而忽略了不同表征对最终聚类结果的先验知识.为了解决这些问题,本文提出了一种新颖的张量学习诱导的多视图谱聚类(TLIMSC)方法,其中同时探索了空间聚类结构和互补信息.具体来说,该方法将关联样本和簇关系的多视图谱嵌入表示堆叠成张量,计算复杂度最终变为O(n logn).然后,将学习到的带有不同自适应置信度的表征与最终的一致聚类结果联系起来.在五个数据集上的广泛实验证明了TLIMSC所具有的有效性和高效性.

基于加权张量低秩约束的多视图谱聚类

现有基于图的多视图聚类方法通常难以同时考虑不同视图的潜在高阶相关信息和每个视图内的全局几何结构,导致聚类性能受限。为此,提出一种基于加权张量低秩约束的多视图谱聚类方法(WTLR-MSC)。根据多视图数据构建概率转移矩阵,将所有的概率转移矩阵构建为三阶张量,并借助鲁棒主成分分析思想将其分解为目标张量和误差张量。使用加权张量核范数约束目标张量的旋转张量,利用奇异值先验信息准确挖掘多视图数据的潜在高阶相关信息,并利用核范数约束目标张量的每个正切片以刻画每个视图内的全局几何结构。基于此建立数学模型,并设计有效的求解算法。在BBCSport、BBC4View、COIL20、UCI Digits 4个常用数据集上的实验结果表明,WTLR-MSC较ERLRT、MCA~2M、MGL-WTNN等聚类方法的性能有显著提升,准确率、标准化互信息、F1值、精确率、召回率相较于次优方法最高提升约1.3、1.0、1.2、1.6和0.8个百分点,大幅增强了多视图聚类的稳健性。

Weighted norm inequalities for the multilinear Calderón-Zygmund operators

In this paper, by proving some suitable weighted endpoint estimates, and then by multilinear interpolation and a new multilinear extrapolation lemma, the author establishes some weighted estimates for the multilinear Calderón-Zygmund operator. Also, the author gives a weighted estimate for the corresponding commutator.