H1(Rn)的极大函数特征

当ψ(x),x∈R^n满足较弱的大小和光滑性条件时，本文证明了由它定义的极大函刻画了Hardy空间H^1(R^n）。     

CONTINUITY FOR MAXIMAL COMMUTATORS OF BOCHNER-RIESZ OPERATORS WITH BMO FUNCTIONS

1 IntroductionLet b E BMO(R") and let T be a standard Calder6n--Zygnmnd operator. The commutator[6, T generated by b and T is defined by[5, T]f(x) = b(x)Tf(x) -- T(5f)(x).A famous result of Coifmau, Rochberg and Weiss in [1] states that the operator [6, T] is boundedon Lp(R") for p E (1,oc). It is well-known that the standard Calder6n-Zygmund singularintegrals map continuously HP(R"), the standard Hardy space, into Lp(R") and HP,co (R" ),the standaxd weak Hardy space, into LPtco(…     

B-(p,r)-不变凸规划问题的Mond-Weir型对偶

利用一类新的广义凸函数:B- (p,r) -不变凸函数,建立了多目标规划问题的Mond- Weir型对偶,证明了弱对偶、强对偶和逆对偶定理.其结论具有一般性,推广了许多涉及不变凸函数、不变B-凸函数和(p,r) -不变凸函数的文献的结论.     

单边Hardy－Littlewood极大算子的加权弱（1．1）型不等式

设Ｍ￣＋、Ｍ￣－为单边Ｈａｒｄｙ－Ｌｉｔｔｌｅｗｏｏｄ极大算子，ｕ（ｘ）、ｖ（ｘ）为实直线Ｒ上两个权函数。本文得到Ｍ￣＋（或Ｍ￣－）关于测度ｖ（ｘ）ｄｘ和ｕ（ｘ）ｄｘ是弱（１．１）型的当且仅当（ｕ，ｖ）∈或（ｕ，ｖ）．     

$(p,q)$-Analogue of Mittag-Leffler Function with $(p,q)$-Laplace Transform

The aim of this paper is to define $(p, q)$-analogue of Mittag-Leffler Function, by using $(p, q)$-Gamma function. Some transformation formulae are also derived by using the $(p, q)$-derivative. The $(p, q)$-analogue for this function provides elegant generalization of $q$-analogue of Mittag-Leffler function in connection with $q$-calculus. Moreover, the $(p, q)$-Laplace Transform of the Mittag-Leffler function has been obtained. Some special cases have also been discussed.     

弱型及加权弱拟(1,1)型算子的有界性

在这篇文章中 ,我们介绍了拟 (1 ,1 )型算子T ,给出了它的弱有界性和加权弱有界性     

General Wentzell Boundary Conditions and Analytic Semigroups on W 1, p (0, 1)

We are concerned with the analyticity of the (C ₀) semigroups generated by the realizations of the Laplacian Δu:=u″ in the spaces C[0, 1] and W ^{1, p} (0, 1) with the general Wentzell boundary conditions Δu(j)+β ^ju″(j)+γ _ju(j)=0 for j=0,1. Here 1<p<∞ and β _j , γ _j are arbitrary complex numbers for j=0,1.     

在空间W_0~(1，x)L~(P(x))(Q)及其共轭空间中的若干收敛性定理

本文证明了在空间W_0~(1,x)L~(p(x))(Q)及其共轭空间中三个收敛性定理.在附加较弱条件的情况下,给出了几乎处处收敛蕴含弱收敛,弱收敛蕴含强收敛.     

半平面上的Dirichlet级数的$(p,q)(R)$级和$(p,q)(R)$下级

讨论半平面上的Dirichlet级数的(p,q)(R)级,(p,q)(R)下级和正规(p,q)(R)级及它们之间的联系,并讨论了(p,q)(R)级,(p,q)(R)下级与级数的指数之间的关系.     

Dual Lie Bialgebra Structures of W -algebra W (2, 2) Type

In the present paper, we investigate the dual Lie coalgebras of the centerless W(2, 2) algebra by studying the maximal good subspaces. Based on this, we construct the dual Lie bialgebra structures of the centerless W(2, 2) Lie bialgebra. As by-products, four new infinite dimensional Lie algebras are obtained.     

含p(x)-Laplacian算子的Neumann问题解的存在性

利用极大单调算子理论,给出了一类含p(x)-Laplacian算子的Neumann边值问题解的存在的充分条件.讨论用到了Lp(x)(Ω)和W01,p(x)(Ω)空间的理论.     

TWO ENTIRE FUNCTIONS SHARING FOUR SMALL FUNCTIONS IN THE SENSE OF (E-)k)(β, f)= (E-)k)(β,g)

This paper proves a result that if two entire functions f(z) and g(z) share foursmall functions aj (z) (j = 1,2, 3, 4) in the sense of Ek) (aj, f) = Ek)(aj, g), (j = 1, 2, 3, 4)(k ≥ 11), then there exists f(z) = g(z).     

W~m_2(R~n)中单个函数的平移和伸缩组合的稠密性

本文讨论单个函数的平移和伸缩的组合在Ｓｏｂｏｌｅｖ空间Ｗ２Ｍ（Ｒｎ）中稠密的问题,得到了稠密的一个充分必要条件,并对于Ｗ２ｍ（Ｒｎ）中紧集内的函数给出更强的逼近结果。     

基于鞅空间M(ln~+M)~p,L(ln~+L)~p与K(ln~+K)~p的关系研究

旨在利用概率方法探讨鞅空间K2与M1之间的鞅空间包含变化关系.首先提出了新的鞅空间M(ln+M)p,L(ln+L)p以及K(ln+K)p(其中p 1)的定义,并证明了其空间包含关系.     

On two (p,q)-analogues of the Laplace transform

Two (p, q)-Laplace transforms are introduced and their relative properties are stated and proved. Applications are made to solve some (p, q)-linear difference equations.     

(p,Y)-算子框架的稳定性

In this paper we study the stability of（p,Y）-operator frames.We firstly discuss the relations between p-Bessel sequences（or p-frames） and（p,Y）-operator Bessel sequences（or（p,Y）-operator frames）.Through defining a new union,we prove that adding some elements to a given（p,Y）-operator frame,the resulted sequence will be still a（p,Y）-operator frame.We obtain a necessary and sufficient condition for a sequence of compound operators to be a（p,Y）operator frame.Lastly,we show that（p,Y）-operator frames for X are stable under some small perturbations.     

(p,q)‐Generalization of Szász–Mirakyan operators

In this paper, we introduce new modifications of Szász–Mirakyan operators based on (p,q)‐integers. We first give a recurrence relation for the moments of new operators and present explicit formula for the moments and central moments up to order 4. Some approximation properties of new operators are explored: the uniform convergence over bounded and unbounded intervals is established, direct approximation properties of the operators in terms of the moduli of smoothness is obtained and Voronovskaya theorem is presented. For the particular case p = 1, the previous results for q‐Sz ász–Mirakyan operators are captured. Copyright © 2015 John Wiley & Sons, Ltd.     

关于(s,p)-w-亚正常算子类

本文在W-亚正常算子类的基础上，引入（s，p）-w-亚正常算子类，进而讨论了该类算子的特征，包含关系，对一类特殊的该类算子还考虑了其平方性质．     

p(x)-Laplace方程的强极大值原理

本文给出了如下形式的p(x)-Laplace方程 -div(|u|~(p(x)-2)u)+d(x)|u|~q(x)-2)u=0,x∈Ω的一个强极大值原理,其中p(x),q(x),d(x)满足一定的条件。     

弱(L_1,L_2)-BLD映射的正则性

本文首先将文［１］中的ＢＬＤ映射推广为弱（Ｌ１，Ｌ２）－ＢＬＤ映射，并证明了如下正则性结果：存在两个可积指数 Ｐ１＝Ｐ１（ｎ，Ｌ１，Ｌ２）＜ｎ＜ｑ１＝ｑ１（ｎ，Ｌ１，Ｌ２），使得对任意弱（Ｌ１，Ｌ２）－ＢＬＤ映射ｆ∈（Ω，Ｒｎ），都有ｆ∈（Ω，Ｒｎ），即ｆ为（Ｌ１，Ｌ２）－ＢＬＤ映射．