Calculus of sequential normal compactness in variational analysis

In this paper we study some properties of sets, set-valued mappings, and extended-real-valued functions unified under the name of “sequential normal compactness.” These properties automatically hold in finite-dimensional spaces, while they play a major role in infinite-dimensional variational analysis. In particular, they are essential for calculus rules involving generalized differential constructions, for stability and metric regularity results and their broad applications, for necessary optimality conditions in constrained optimization and optimal control, etc. This paper contains principal results ensuring the preservation of sequential normal compactness properties under various operations over sets, set-valued mappings, and functions.     

关于L-fuzzy拓扑分离性的弱同胚不变性质

本文研究了一种新的弱同胚不变性质，它更具有一般性；证明了目前文献中所论述的各种分离性都是弱同胚不变性质，并且否定回答了王国俊提出的两个分离性问题。     

齐次群上新Hardy空间的分子特征及其应用

建立了齐次群上伴随于Herz空间和Beurling代数的Hardy空间的分子分解理论．作为其应用．研究了中心强奇异Calderon-Zygmund算子在这些空间上的有界性．     

Equivalent quasi-norms on Lorentz spaces

We give new characterizations of Lorentz spaces by means of certain quasi-norms which are shown to be equivalent to the classical ones.

     

A version of Burkholder's theorem for operator-weighted spaces

Let be an operator weight, i.e. a weight function taking values in the bounded linear operators on a Hilbert space . We prove that if the dyadic martingale transforms are uniformly bounded on for each dyadic grid in , then the Hilbert transform is bounded on as well, thus providing an analogue of Burkholder's theorem for operator-weighted -spaces. We also give a short new proof of Burkholder's theorem itself. Our proof is based on the decomposition of the Hilbert transform into ``dyadic shifts'.

     

On non-measurability of in its second dual

We show that with the weak topology is not an intersection of Borel sets in its Cech-Stone extension (and hence in any compactification). Assuming (CH), this implies that has no continuous injection onto a Borel set in a compact space, or onto a Lindelöf space. Under (CH), this answers a question of Arhangel'ski.

     

On Korovkin Type Theorem in the Space of Locally Integrable Functions

It is shown that a Korovkin type theorem for a sequence of linear positive operators acting in weighted space L _p,w (loc) does not hold in all this space and is satisfied only on some subspace.     

New minimax inequality with applications to existence theorems of equilibrium points

A new minimax inequality is proved on a set which is the union of an increasing sequence of compact convex sets in a topological vector space. As applications, several existence theorems of equilibrium points for different games are obtained.The authors would like to thank the referees for their helpful suggestions.     

Cramér theorem on symmetric spaces of noncompact type

We prove the Cramér theorem forK-invariant Gaussian measures on irreducible symmetric spacesX=G/K withG semisimple noncompact. To do this we use a kind of Abel transform ofK-invariant measures onX.This research is supported by KBN Grant.     

Analytic Atomic Screening Parameters for Slater Type Orbitals

Screening parameters to be used in Slater Type Orbitals were obtained in analytic form. The values compared well with the numerical results given by Clementi and Roetti (after a laborious process of optimization) and with the phenomenological values of Jung and Gould. The analytic formulation is based on the splitting of the two-body operator 1/r_st as the sum of effective one-body operators.