上半空间中一类次调和函数的增长估计

本文证明了n-维(n≥2)Euclidean空间的上半空间中Poisson积分在无穷远点处的增长性质.同时将这个性质推广到次调和函数中去,其概括了解析函数和调和函数的增长性质.     

一个Chern—Kuiper型的不可浸入性定理

本文建立了一个新的Chern-Kuiper型的不可浸入性定理.假设M是一个n-维紧致的黎曼流形,M的Ricci和数量曲率R满足Ric+R≥0andR＞n(n-1)λ-2,则M不能等距地浸入在欧氏空间Rn+1的半径为λ的闭球中.从而推广了Deshmukh和Al-Gwaiz的结果.     

H1中(次)临界的复Ginzburg-Landau方程解的长时间行为

研究H1(Rn)中临界的复Ginzburg-Landau方程的初值问题,当空间维数n≥3时,讨论了它的解在空间C(0,oo;H1(Rn))∩ L2(0,∞;H1,2n/(n-2)(Rn))的长时间衰减行为.当空间维数n≥1时,对非线性项在H1(Rn)中具有次临界的增长阶的情形也有类似的结果.     

半空间中几类多项式与Poisson核乘积的积分及增长性

本文研究了半空间中的几类多项式与Poisson核乘积的积分及其增长性质,通过逐渐减弱收敛条件并重新定义测度的方法,得到了多重调和方程的Dirichlet边值问题解的两种特殊情况,即两类调和多项式与Poisson核乘积的积分的增长性质,推广了半空间中关于修改的Poisson积分的结果.     

半空间中一类推广的Poisson积分的增长性质

本文研究了推广的Poisson积分的增长性问题.利用复平面中经典的Hayman定理及其证明方法,通过修改上半空间中的Poisson积分,获得了上半空间中一类位势在无穷远点的增长性质,推广了Hayman定理在高维空间的结果.     

半空间上与高阶Laplace算子相对应的积分方程组(英文)

利用积分形式的移动平面法,给出n维上半空间R_+~n积分方程组{u(x)rn+(1|x-y|n-a-1|x*-y|n-a)(γ1up1(y)+u1vp2(y)+βup3(y)vp4(y)dyv(x)=rn+(1|x-y|n-a-|x*-y|n-a)(γ1uq1(y)+u2vq2(y)+β2uq3(y)vq4(y)dy}解的单调性和旋转对称性,其中0αn,λ_i,μ_i,β_i≥0(i=1,2)是非负常数,pi,qi(i=1,2,3,4)满足适当的假设,x~*=(x_1,x_2,…,x_(n-1),-x_n)是点x关于超平面x_n=0的反射点.本文的结果推广了n维欧氏空间R~n中的结果.     

一类调和多项式与Poisson核乘积的积分及增长性

本文研究了半空间上的一类调和多项式与Poisson核的乘积的积分及其增长性问题.通过利用已知的收敛条件重新定义测度的方法和相应的增长估计,获得了一类调和多项式与Poisson核乘积的积分的增长性质,推广了关于Poisson积分的结果.     

Δu-a(x)u+b(x)u~p=0奇解的渐近性质

讨论了半线性椭圆方程Δu-a(x)u+b(x)up=0奇解的渐近性质,其中u∶Ω→R,ΩRn,n 3,n/(n-2)相似文献   

一道Lebesgue积分题目的注记

设E为n维欧氏空间Rn的可测子集,m E+∞,f(x)为E上的非负可测函数,并记Ek=E{x|k≤f(x)k+1}(k=0,1,2,…),利用Lebesgue积分的性质,通过构造反例,指出"级数∑k km Ek收敛"并不是f(x)在E上Lebesgue可积的充分条件.进一步,通过增加条件"f在E上a.e.有限",得到相应的充分必要条件.     

Kubota公式的注记

本文研究了n维欧式空间中En中r-维平面的密度与(n-1)维球的体积元之间的关系.利用了复合叠加等的方法,得到了n维欧式空间En的凸体和任意n-r维投影空间Ln-r之间均值积分的关系,推广了Kubota公式得到的结果     

极大奇异积分算子的一个BLO估计

本文研究以(Ω(x)/|z|n))为核的极大齐次奇异积分算子在空间BMO(R~n)上的性质,其中Ω是一个零阶齐次函数且在单位球面上均值为零．可以证明：若Ω满足某种最小尺度条件和某种L~1-Dini型正则性条件,则此极大奇异积分算子是由BMO(R~n)到BLO(R~n)的有界算子．     

Symmetry and regularity of solutions to a system with three-component integral equations

Consider the system with three-component integral equations u(x) = Rn |x y|α nw(y)rv(y)q dy,v(x) = Rn |x y|α nu(y)pw(y)rdy,w(x) = Rn |x y|α nv(y)q u(y)pdy,where 0 < α < n,n is a positive constant,p,q and r satisfy some suitable conditions.It is shown that every positive regular solution(u(x),v(x),w(x)) is radially symmetric and monotonic about some point by developing the moving plane method in an integral form.In addition,the regularity of the solutions is also proved by the contraction mapping principle.The conformal invariant property of the system is also investigated.     

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）。     

Boundedness of Marcinkiewicz integrals and their commutators in H1(Rn×Rm)

The authors establish the boundedness of Marcinkiewicz integrals from the Hardy space H1(Rn × Rm) to the Lebesgue space L1(Rn × Rm) and their commutators with Lipschitz functions from the Hardy space H1(Rn × Rm) to the Lebesgue space Lq(Rn × Rm) for some q＞1.     

Pointwise Fourier inversion of distributions

We show that,given a tempered distribution T whose Fourier transform is a function of polynomial growth and a point x in Rn at which T has the value τ(in the sense of Lojasiewicz),the Fourier integral of T at x is summable in Bochner-Riesz means to τ.     

Compactness for the commutators of multilinear singular integral operators with non-smooth kernels

In this paper, the behavior for commutators of a class of bilinear singular integral operators associated with non-smooth kernels on the product of weighted Lebesgue spaces is considered. By some new maximal functions to control the commutators of bilinear singular integral operators and CMO(Rn) functions, compactness for the commutators is proved.     

强奇异积分算子交换子的端点估计

本文考虑强奇异积分算子的交换子在Hardy型空间上的端点估计,建立了这类交换子从H¹（Rⁿ）到弱 L¹（Rⁿ）上的有界性及H¹（Rⁿ）的某个子空间到 L¹（Rⁿ）上的有界性结果.     

半平面中解析函数的积分表示及在逼近中的应用

在该文中, 作者证明了满足一定增长性条件的右半平面上的解析函数可以由它在边界上的积分和其加权Blaschke乘积的和表示, 作为应用, 作者还考虑了指数多项式在实数轴上加权 Banach 空间C_α 中的完备性.     

Some Oscillatory Singular Integrals on Herz-type Spaces (Ⅱ)

In this paper, the authors prove that some oscillatory singular integral operators of non-convolution type with non-polynomial phases are bounded from the Herz-type Hardy spaces to the Herz spaces and from the Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions, even though it is well-known that these operators are not bounded from the Hardy space H1(Rn) into the Lebesgue spaceL1(Rn).     

Integral representation and estimation of harmonic functions in the quaternionic half space

In this article, we discuss the integral representation of quaternionic harmonic functions in the half space with the general boundary condition. Next, we derive a lower bound from an upper one for quaternionic harmonic functions. These results generalize some of the classic results from the case of plane to the case of noncommutative quaterninionic half space. Copyright © 2017 John Wiley & Sons, Ltd.