关于σ-有限测度空间的Loeb空间的一点注记

以一种自然的方式定义了σ－有限测度空间的Loeb空间，并研究了其若干性质，将有限Loeb测定空间的一些重要性质推广到σ－有限情形，并将Loeb测度对有限Radon测度的刻画定理推广到σ－有限情形。     

关于算子空间逼近性质的一个注记

考虑算子空间和C*-代数的算子空间逼近性质,强箅子空间逼近性质与分片映射性质之间的某些关系.     

关于属性测度空间粗糙集模型的一个注记

文[1]关于属性粗糙集的定义中,上、下近似算子分别由等价类中元素属性测度的上、下确界来确定,没有充分反映等价类中其它元素的作用,在信息处理中不免造成元素信息的丢失。为此提出一种新的属性粗糙集近似算子的表示方法,给出了相应的性质,并实例说明了这一方法的合理性。     

关于Volterra积分方程的一个注记

使用Monch不动点定理，得到模糊Volterra积分方程模糊解的存在性。     

关于Herz型空间中加权Hardy-Littlewood平均的一个注记

本文给出了加权Hardy-Littlewood平均在Herz型空间中关于权有界的充分必要条件.     

关于Poincare级数算子的范数的一个注记

设无挠Ｆｕｃｈｓ群Г及其子群Г对应的Ｐｏｉｎｃａｒｅ给数算子为Г／Г，对于Г的Ｔｅｉｃｈｍｕｌｅｒ空间Ｔ（Г）中的任意一点「ｆ」，有相应的算子Гｆ／Гｆ，其中Гｆ＝ｆГｆ＾－１，从而Гｆ／Гｆ的范数‖Гｆ／Гｆ‖为Ｔ（Г）上的函数，众所周知‖Гｆ／Гｆ‖≤１，本文证明了在整个Ｔ（Г）上‖Гｆ／Гｆ‖没有小于１的上界。     

关于Herz型空间中加权Hard-Littlewood平均的一个注记

本文给出了加权Hardy-Littlewood平均在Herz型空间中关于权有界的充分必要条件.     

带非双倍测度的BMO空间的一个注记

Let μ be a positive Radon measure which only satisfies an appropriate growth condition, and RBMO(μ) be the BMO space associated with μ which was introduced by Tolsa. In this paper, it is proved that the definition of RBMO(p) can be weakened sufficiently.Key words: RBMO(μ); non doubling measure; doubling cube     

关于算子多项式的一点注记

本注记应用Ｇｅｌｆａｎｄ表示定理，推广了文「１，２」中关于算子多项式正性的两个主要结果，并且给出更直接和简单和证明。     

A Characterization of Vanishing Mean Oscillation

We show that a function has vanishing mean oscillation with respect to a nonatomic measure if and only if it satisfies an asymptotic reverse Jensen inequality.     

A Characterization of Vanishing Mean Oscillation

We show that a function has vanishing mean oscillation with respect to a nonatomic measure if and only if it satisfies an asymptotic reverse Jensen inequality.     

Carleson conditions for asymptotic weights

The doubling and conditions are characterized in terms of convolution with rapidly decreasing kernels. The Carleson-measure criterion for of Fefferman, Kenig, and Pipher is extended to the case when all bounds become optimally small in the asymptotic limit.

     

有界平均振幅空间上的乘法算子

有界平均振幅空间的研究在算子理论及全纯空间的研究中具有重要的作用.主要研究了有界平均振幅空间上乘法算子的性质,并且得到了托普里兹算子有界性及紧性的条件.     

Correction to ``Optimal factorization of Muckenhoupt weights'

Peter Jones' theorem on the factorization of  weights is sharpened for weights with bounds near , allowing the factorization to be performed continuously near the limiting, unweighted case. When and is an  weight with bound , it is shown that there exist  weights  such that both the formula and the estimates hold. The square root in these estimates is also proven to be the correct asymptotic power as .

     

Optimal factorization of Muckenhoupt weights

Peter Jones' theorem on the factorization of  weights is sharpened for weights with bounds near , allowing the factorization to be performed continuously near the limiting, unweighted case. When and is an  weight with bound , it is shown that there exist  weights  such that both the formula and the estimates hold. The square root in these estimates is also proven to be the correct asymptotic power as .

     

Parabolic Equations with Measurable Coefficients

We investigate the unique solvability of second order parabolic equations in non-divergence form in , p ≥ 2. The leading coefficients are only measurable in either one spatial variable or time and one spatial variable. In addition, they are VMO (vanishing mean oscillation) with respect to the remaining variables. The second author was partially supported by NSF Grant DMS-0140405.     

Vanishing Cycles of Irregular D-Modules

Considering a holonomic -module and a hypersurface, we define a finite family of -modules on the hypersurface which we call modules of vanishing cycles. The first one had been previously defined and corresponds to formal solutions. The last one corresponds, via Riemann-Hilbert, to the geometric vanishing cycles of Grothendieck-Deligne. For regular holonomic -modules there is only one sheaf and for non regular modules the sheaves of vanishing cycles control the growth and the index of solutions. Our results extend to non holonomic modules under some hypothesis.     

消失的弱~Morrey 型空间上某些算子的刻画

In this paper we mainly give some characterizations for the boundedness of the weight Hardy operator, maximal operator, potential operator and singular integral operator on the vanishing generalized weak Morrey spaces V W L_Π~(p,φ)(?) with bounded set ?.