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.

两类加权空间间的积分算子与离散算子的有界性及算子范数估计

Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space.

Norms of Dual Complex Vectors and Dual Complex Matrices

In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder inequality,and the Minkowski inequality in the setting of dual complex numbers.Second,we define the p-norm of a dual complex vector,which is a nonnegative dual number,and show some related properties.Third,we study the properties of eigenvalues of unitary matrices and unitary triangulation of arbitrary dual complex matrices.In particular,we introduce the operator norm of dual complex matrices induced by the p-norm of dual complex vectors,and give expressions of three important operator norms of dual complex matrices.

ON THE BOUNDEDNESS AND THE NORM OF A CLASS OF INTEGRAL OPERATORS

The boundedness and the norm of a class of integral operators Ta,b,c on Lλ^P spaces are studied in this paper. The author not only gives the sufficient and necessary condition for the boundedness of Ta,b,c on Lλ^P,but also obtains its accurate norm on Lλ^P for some range under the condition of c = n ＋ a ＋ b.

A Non-Archimedean Version of the Classical Hilbert Inequality

In this note, we introduce and study a p-adic Hilbert-type integral operator and obtain its sharp norm estimate. As applications, we establish a p-adic Hilbert-type inequality with the best constant and its equivalent form.

A RECURSIVE ALGORITHM AND ITS CONVERGENCE FOR PARAMETER ESTIMATION OF CONVOLUTION MODEL

In this article, the problem on the estimation of the convolution model parameters is considered. The recursive algorithm for estimating model parameters is introduced from the orthogonal procedure of the data, the convergence of this algorithm is theoretically discussed, and a sufficient condition for the convergence criterion of the orthogonal procedure is given. According to this condition, the recursive algorithm is convergent to model wavelet A- = （1, α1,..., αq）.

ON PROBABILISTIC NORM OF A LINEAR OPERATORS AND SPACE OF OPERATORS

Since the PN space (E, F) which satisfies condition (PN-5) is just a Menger PN-space (E, F, min), the results with regard to probabilistic norms of linear operators on PN-spaces obtained by Xiao Jianzhong have bigger limitations. In this paper, problems respecting probabilistic norms of linear operators and spaces of operators are studied on more general Menger PN-spaces. The results presented improve and generalize the corresponding results by Xiao.

The Optimal Matching Parameter of Half Discrete Hilbert Type Multiple Integral Inequalities with Non-Homogeneous Kernels and Applications

By using the weight function method,the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K(n,||x||ρ,m)=G(nλ1||x||ρmλ,2)are discussed,some equivalent conditions of the optimal matching parameter are established,and the expression of the optimal constant factor is obtained.Finally,their applications in operator theory are considered.

Parameter Conditions for Hilbert-Type Operator Bounded with Homogeneous Kernels between Sequence Space l and Function Space L

By using the technique of real analysis,the parameter conditions for Hilberttype series operator and integral operator T_(1)(˜a)(x)=∑∞n=1 K(n,x)a_(n),T_(2)(f)_(n)=∫+∞0 K(n,x)f(x)dx.bounded with homogeneous kernels are discussed.The necessary and sufficient conditions for T_(1):l^(α)_(p)→L^(β)_(p)^((1−p))p(0,+∞)and T_(2):L_(q)^(β)(0,+∞)→l^(α(1−q))_(q)bounded are obtained,and their norm expressions are established under certain conditions.

Berry-Esseen bounds and moderate deviations for the norm, entries and spectral radius of products of positive random matrices

Let(g_(n))_(n≥1) be a sequence of independent and identically distributed positive random d×d matrices and consider the matrix product G_(n)=g_(n)…g_1.Under suitable conditions,we establish the Berry-Esseen bounds on the rate of convergence in the central limit theorem and Cramer-type moderate deviation expansions,for any matrix norm ‖G_(n)‖ of G_(n),its entries G_(n)^(i,j) and its spectral radius ρ(G_(n)).Extended versions of their joint law with the direction of the random walk G_(n)x are also established,where x is a starting point in the unit sphere of R~d.

Complementary Inequalities to Improved AM-GM Inequality

Following an idea of Lin, we prove that if A and B are two positive operators such that 0 〈 mI 〈 A 〈 m＇I ≤ M＇I ≤B 〈 MI, then Ф^2（A＋B/2）≤K^2（h）/（1＋（logM＇/m＇）^2/8）^2Ф^2（A#B）,and Ф^2（A＋B/2）≤K^2（h）/（1＋（logM＇/m＇）^2/8）^2（Ф（A）#Ф（B））^2,where K（h） = （h＋1）2 /4h and h = M and Ф is a positive unital linear map.

Weighted Norm Inequalities for Some Singular Integral Operators

In this paper,we consider the related weighted boundedness of the operators which were studied by J.Duoandikotxea and J.L.Ruhio de Francia.

Remarks on the Operator Norm Localization Property

The author studies the metric spaces with operator norm localization property. It is proved that the operator norm localization property is coarsely invariant and is preserved under certain infinite union. In the case of finitely generated groups, the operator norm localization property is also preserved under the direct limits.

A Quantitative Version of the Bishop–Phelps Theorem for Operators in Hilbert Spaces

In this paper, with the help of spectral integral, we show a quantitative version of the Bishop-Phelps theorem for operators in complex Hilbert spaces. Precisely, let H be a complex Hilbert space and 0 〈 s 〈 1/2. Then for every bounded linear operator T ： H → H and x0 ∈ H with ｜｜T｜｜ = 1 = ｜｜xo｜｜ such that ｜｜Txo｜｜ 〉 1-6, there exist xε ∈ H and a bounded linear operator S ： H → H with ｜｜S｜｜ = 1 = ｜｜xε｜｜ such that ｜｜Sxε｜｜=1, ｜｜x-ε0｜｜≤√2ε＋4√2ε, ｜｜S-T｜｜≤√2ε.

New Developments on Operator Reverse AM-GM Inequality for Positive Linear Maps

In this research article,we shall give some reverse Arithmetic-Geometric mean inequalities for unital positive linear maps on Hilbert space operators under some different conditions.Our results are sharper and more precise as compared to some recent published results.Moreover,we shall present refinements of the Lin conjecture.