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1.
In this paper, some endpoint estimates for the generalized multilinear fractional integrals I_(α,m) on the non-homogeneous metric spaces are established.  相似文献   
2.
For a general dyadic grid, we give a Calderón–Zygmund type decomposition, which is the principle fact about the multilinear maximal function on the upper half‐spaces. Using the decomposition, we study the boundedness of . We obtain a natural extension to the multilinear setting of Muckenhoupt's weak‐type characterization. We also partially obtain characterizations of Muckenhoupt's strong‐type inequalities with one weight. Assuming the reverse Hölder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hytönen–Pérez type weighted estimates.  相似文献   
3.
设A是Rn上的各向异性伸缩, L是由各向异性Calderón-Zygmund算子生成的一般的多线性算子.本文得到L从加权Lebesgue空间Lwp(Rn)到无权的各向异性Hardy空间HAp (Rn)的有界性.另外,对各向异性Hardy空间H1(Rn)和加权各向异性BMO空间BMOAw(Rn)得到包含关系:BMOAw(Rn)■(H1A(Rn))*.作为应用,对加权各向异性BMO函数b和各向异性Calderón-Zygmund算子T生成的交换子[T, b],得到‖[T, b](f)‖Lwp(Rn)C‖b‖BMOwA(Rn)‖f‖Lpw(Rn).以上所有结果在经典的各向齐性情形下也是新的.  相似文献   
4.
This paper is devoted to the high-dimensional and multilinear Hausdorff operators on the Heisenberg group H n. The sharp bounds for the strong type(p, p)(1 ≤ p ≤∞) estimates of n-dimensional Hausdorff operators on H n are obtained. The sharp bounds for strong(p, p) estimates are further extended to multilinear cases. As an application, we derive the sharp constant for the multilinear Hardy operator on H n. The weak type(p, p)(1 ≤ p ≤∞) estimates are also obtained.  相似文献   
5.
Isoquercitrin is a flavonoid chemical compound that can be extracted from different plant species such as Mangifera indica (mango), Rheum nobile , Annona squamosal , Camellia sinensis (tea), and coriander ( Coriandrum sativum L.). It possesses various biological activities such as the prevention of thromboembolism and has anticancer, antiinflammatory, and antifatigue activities. Therefore, there is a critical need to elucidate and predict the qualitative and quantitative properties of this phytochemical compound using the high performance liquid chromatography (HPLC) technique. In this paper, three different nonlinear models including artificial neural network (ANN), adaptive neuro-fuzzy inference system (ANFIS), and support vector machine (SVM),in addition to a classical linear model [multilinear regression analysis (MLR)], were used for the prediction of the retention time (tR) and peak area (PA) for isoquercitrin using HPLC. The simulation uses concentration of the standard, composition of the mobile phases (MP-A and MP-B), and pH as the corresponding input variables. The performance efficiency of the models was evaluated using relative mean square error (RMSE), mean square error (MSE), determination coefficient (DC), and correlation coefficient (CC). The obtained results demonstrated that all four models are capable of predicting the qualitative and quantitative properties of the bioactive compound. A predictive comparison of the models showed that M3 had the highest prediction accuracy among the three models. Further evaluation of the results showed that ANFIS–M3 outperformed the other models and serves as the best model for the prediction of PA. On the other hand, ANN–M3proved its merit and emerged as the best model for tR simulation. The overall predictive accuracy of the best models showed them to be reliable tools for both qualitative and quantitative determination.  相似文献   
6.
In this article we explore the notion of everywhere almost summing polynomials and define a natural norm which makes this class a Banach polynomial ideal which is a holomorphy type and also coherent and compatible with the notion of almost summing linear operators. Similar results are not valid for the original concept of almost summing polynomials, due to G. Botelho.  相似文献   
7.
在p-adic域上研究分数次Hardy型算子与CMO(Q_p~n)函数生成的多线性交换子,建立了交换子在Lebesgue空间和Herz空间上的有界性.对Hardy算子的多线性交换子也得到了相应的结果.  相似文献   
8.
《分析论及其应用》2015,(3):244-252
For the commutators of multilinear Calder ′on-Zygmund singular integral operators with B MO functions, the weak type weighted norm inequalities with respect to A~P weights are obtained.  相似文献   
9.
多线性分离变量法已成功地应用于诸多(2+1)维非线性可积系统.将该方法拓展运用于(3+1)维破碎孤子方程中,获得了含任意函数的变量分离解.通过适当地设定任意函数的形式,得到了(3+1)维破碎孤子方程丰富的局域激发模式.  相似文献   
10.
对任意给定的正整数m,Z^+×{1,...,m}的任意一个有限子集S,定义一般化的多线性分数次积分算子的交换子Iα,→b,S(f)(x)=∫(Rn)^m ∏(i,j)∈S(bi(x)-bi(yj))/(|x-y1|+…+|x-ym|)^mn-α∏(j=1→m)fj(yj)d→y,其中d→y=dy1…dym.此框架下的交换子包含了以往研究的各类分数次积分算子的交换子,并蕴含了多线性背景下新的交换子形式.在上述非常一般框架下,本文给出带多重A→p,q权的多线性分数次积分算子的交换子Iα,→b,S(→f)的加权强型(L^p1(ω1)×···×L^pm(ωm),L^q(ν→ωq))估计和加权弱型端点估计.本文还得到更一般核条件下的上述结果.  相似文献   
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