CARLESON MEASURES FOR BESOV-SOBOLEV SPACES WITH APPLICATIONS IN THE UNIT BALL OF C^n

This paper is devoted to give the connections between Carleson measures for Besov-Sobolev spaces Bσp (B) and p-Carleson measure in the unit ball of Cn. As appli-cations, we characterize the Riemann-Sti...     

A 2-block semi-proximal ADMM for solving the H-weighted nearest correlation matrix problem

Higham considered two types of nearest correlation matrix (NCM) problems, namely the W-weighted case and the H-weighted case. Since there exists well-defined computable formula for the projection onto the symmetric positive semidefinite cone under the W-weighting, it has been well studied to make several Lagrangian dual-based efficient numerical methods available. But these methods are not applicable for the H-weighted case mainly due to the lack of a computable formula. The H-weighted case remains numerically challenging, especially for the highly ill-conditioned weight matrix H. In this paper, we aim to solve the dual form of the H-weighted NCM problem, which has three separable blocks in the objective function with the second part being linear. Based on the linear part, we reformulate it as a new problem with two separable blocks, and introduce the 2-block semi-proximal alternating direction method of multipliers to deal with it. The efficiency of the proposed algorithms is demonstrated on the random test problems, whose weight matrix H are highly ill-conditioned or rank deficient.     

The Singular Function Boundary Integral Method for singular Laplacian problems over circular sections

The Singular Function Boundary Integral Method (SFBIM) for solving two-dimensional elliptic problems with boundary singularities is revisited. In this method the solution is approximated by the leading terms of the asymptotic expansion of the local solution, which are also used to weight the governing partial differential equation. The singular coefficients, i.e., the coefficients of the local asymptotic expansion, are thus primary unknowns. By means of the divergence theorem, the discretized equations are reduced to boundary integrals and integration is needed only far from the singularity. The Dirichlet boundary conditions are then weakly enforced by means of Lagrange multipliers, the discrete values of which are additional unknowns. In the case of two-dimensional Laplacian problems, the SFBIM converges exponentially with respect to the numbers of singular functions and Lagrange multipliers. In the present work the method is applied to Laplacian test problems over circular sectors, the analytical solution of which is known. The convergence of the method is studied for various values of the order p of the polynomial approximation of the Lagrange multipliers (i.e., constant, linear, quadratic, and cubic), and the exact approximation errors are calculated. These are compared to the theoretical results provided in the literature and their agreement is demonstrated.     

Periodic solutions of neutral fractional differential equations

We characterize the existence of periodic solutions for some abstract neutral functional fractional differential equations with finite delay when the underlying space is a UMD space.     

Heisenberg群上与Schrödinger算子相关的Riesz变换在Hardy空间上的有界性

令L=?ΔHn+V是Heisenberg群Hn上Schr?dinger算子,其中非负位势V属于逆H?lder类.该文用分子刻画与L相关的Hardy型空间HL^p(H^n),进而得到了与L相关的Riesz变换的HL^p-有界性.     

Use of Augmented Lagrangian Methods for the Optimal Control of Obstacle Problems

We investigate optimal control problems governed by variational inequalities involving constraints on the control, and more precisely the example of the obstacle problem. In this paper, we discuss some augmented Lagrangian algorithms to compute the solution.     

The optimality conditions for optimization problems with fuzzy-valued objective functions

The optimality conditions for an optimization problem with fuzzy-valued objective function are derived in this article. The solution concept of this optimization problem will follow the similar solution concept, called nondominated solution, in multiobjective programming problem. In order to consider the differentiation of fuzzy-valued function, we invoke the Hausdorff metric to define the distance between two fuzzy numbers and the Hukuhara difference to define the difference of two fuzzy numbers. Under these settings, the optimality conditions for obtaining the nondominated solutions are elicited naturally by introducing the Lagrange multipliers.     

Carleson measures for Besov spaces on the ball with applications

Carleson and vanishing Carleson measures for Besov spaces on the unit ball of are characterized in terms of Berezin transforms and Bergman-metric balls. The measures are defined via natural imbeddings of Besov spaces into Lebesgue classes by certain combinations of radial derivatives. Membership in Schatten classes of the imbeddings is considered too. Some Carleson measures are not finite, but the results extend and provide new insight to those known for weighted Bergman spaces. Special cases pertain to Arveson and Dirichlet spaces, and a unified view with the usual Hardy-space Carleson measures is presented by letting the order of the radial derivatives tend to 0. Weak convergence in Besov spaces is also characterized, and weakly 0-convergent families are exhibited. Applications are given to separated sequences, operators of Forelli–Rudin type, gap series, characterizations of weighted Bloch, Lipschitz, and growth spaces, inequalities of Fejér–Riesz and Hardy–Littlewood type, and integration operators of Cesàro type.