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.     

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.     

Nondeterminism of Linear Operators and Lower Entropy Estimates

Let u be a (bounded, linear) operator from a Hilbert space ℋ into the Banach space C(T), the space of continuous functions on the compact metric space T. We introduce and investigate numbers τ _n (u), n≥1, measuring the degree of determinism of the operator u. The slower τ _n (u) decreases, the less determined are functions in the range of u by their values on a certain set of points. It is shown that n ^−1/2 τ _n (u)≤2e _n (u), where e _n (u) are the (dyadic) entropy numbers of u. Furthermore, we transform the notion of strong local nondeterminism from the language of stochastic processes into that of linear operators. This property, together with a lower entropy estimate for the compact space T, leads to a lower estimate for τ _n (u), hence also for e _n (u). These results are used to prove sharp lower entropy estimates for some integral operators, among them, Riemann–Liouville operators with values in C(T) for some fractal set T. Some multi-dimensional extensions are treated as well.      

Calculus of variations with fractional derivatives and fractional integrals

We prove the Euler–Lagrange fractional equations and the sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann–Liouville.     

The Inverse Spectral Problem for the Sturm-Liouville Operators with Discontinuous Coefficients

We study the inverse spectral problem for the Sturm–Liouville operator whose piecewise constant coefficient A(x) has discontinuity points x _k , k=1,...,n, and jumps A _k =A(x _k +0)/A(x _k -0). We show that if the discontinuity points x ₁,...,x _n are noncommensurable, i.e., none of their linear combinations with integer coefficients vanishes; then the spectral function of the operator determines all discontinuity points x _k and jumps A _k uniquely. We give an algorithm for finding x _k and A _k in finitely many steps.     

Weighted Estimates for the Integral Operators with Monotone Kernel on a Half-Axis

We give criteria for the boundedness of integral operators with nonnegative monotone kernel in the weighted Lebesgue spaces on a half-axis.     

Solution of Some Weight Problems for the Riemann–Liouville and Weyl Operators

The necessary and sufficient conditions are found for the weight function v, which provide the boundedness and compactness of the Riemann–Liouville operator R from L ^p to . The criteria are also established for the weight function w, which guarantee the boundedness and compactness of the Weyl operator W from to L ^q.     

多线性Calder(o)n-Zygmund算子的加权估计

本文建立由Grafakos和Torrea引进的多线性Calder(o)n-Zygmund算子相关极大算子的加权Lp(RN)估计和弱端点估计.     

多线性Calderón-Zygmund算子的加权有界性

建立了多线性Calderón-Zygmund算子在比幂权空间更一般的Herz空间和Herz型Hardy空间上的有界性.作为推论,得到了该算子的幂权估计.在这些幂权估计中,权指标可以突破Ap权的指标限制,显示出和经典Calderón-Zygmund算子本质的区别.     

Sharp Weighted Estimates for a Class of $n$-Dimensional Hardy-Steklov Operators

In this paper, we study one class of $n$-dimensional Hardy-Steklov operators which has important applications in the technical analysis in equity markets. We establish their weighted boundedness and the corresponding operator norms on both $L^p (\boldsymbol{R}^n)$ and BMO($\boldsymbol{R}^n$).     

Sharp Weighted Estimates for a Class of n-dimensional Hardy-Steklov Operators

In this paper, we study one class of n-dimensional Hardy-Steklov operators which has important applications in the technical analysis in equity markets. We establish their weighted boundedness and the corresponding operator norms on both LP（Rn） and BMO（Rn）.     

Estimates for the Approximation Numbers of One Class of Integral Operators. II

We obtain estimates for the Schatten–von Neumann norms of the approximation numbers of Hardy integral operator with variable limits of integration.     

加权复合算子在Bloch型空间上的有界性

In this paper,we give a necessary and sufficient condition for weighted composition operators Cu,ψ to be boundedness on Bloch type spaces Ba.The theorem generalizes some previous results.     

Continuity of Multilinear Operators in Weighted Herz Spaces with Extreme Exponents

Continuity is obtained of some multilinear operators related to certain integral operators for the weighted Herz spaces with extreme exponents. The operators include the Littlewood–Paley and Marcinkiewicz operators.     

多线性分数次积分迭代型交换子的加权不等式

研究了多线性分数次积分算子的迭代型交换子,给出了双权强型不等式的充分条件,即Fefferman -Phong型条件.对此迭代型交换子,还给出了Fefferman-Stein型加权不等式和Coifman型加权不等式.     

Upper Estimates in Direct Inequalities for Bernstein-Type Operators

We obtain explicit upper estimates in direct inequalities with respect to the usual sup-norm distance for Bernstein-type operators. Our approach combines analytical and probabilistic techniques based on representations of the operators in terms of stochastic processes. We illustrate our results by considering some classical families of operators, such as Weierstrass, Szàsz, and Bernstein operators.     

Calderón-Zygmund型算子交换子的加权尖锐估计

本文讨论了θ-型Calderón-Zygmund算子与BMO函数生成的交换子的加权估计.在权函数仅为非负局部可积函数或属于A∞的假设下,当0相似文献   

Volterra Type Operators on Weighted Dirichlet*

The Carleson measures for weighted Dirichlet spaces had been characterized by Girela and Pel′aez, who also characterized the boundedness of Volterra type operators between weighted Dirichlet spaces. However, their characterizations for the boundedness are not complete. In this paper, the author completely characterizes the boundedness and compactness of Volterra type operators from the weighted Dirichlet spaces D^p_α to D^q_β (?1 < α, β and 0 < p < q < ∞), which essentially complete their works. Furthermore, the author investigates the order boundedness of Volterra type operators between weighted Dirichlet spaces.     

核满足弱正则条件的多线性算子交换子的加权估计

本文主要研究核满足弱正则条件的算子与BMO函数生成的多线性交换子.建立了多线性交换子在加权Lebesgue空间的一些性质.     

Some inequalities involving Hadamard‐type k‐fractional integral operators

In this paper, our main aim is to establish some new fractional integral inequalities involving Hadamard‐type k‐fractional integral operators recently given by Mubeen et al. Furthermore, the paper discusses some of their relevance with known results. Copyright © 2017 John Wiley & Sons, Ltd.