一类新型时滞积分不等式及其应用

主要研究了一种新型时滞积分不等式u(t)≤a(t)+∫0α(t)f(t,s)w(u(s))ds+∫0α(t)g(t,s∫)0sh(s,τ)φ(u(τ))dτds up(t)≤a(t)+p/p-q∫0α(t)(f(t,s)uq(s)w(u(s))+g(t,s)uq(s))dsup(t)≤a(t)+p/p-q∫0α(t)f(t,s)uq(s)w(u(s))ds+p/p-q∫0tg(t,s)uq(s)w(u(s))ds这里p>q≥0是常数且t∈[0,∞).并且用此结果研究了时滞微分积分方程解的全局存在性和有界性.     

分数次积分算子的双权弱型赋范不等式

证明了若权函数(u,v)满足下列A_p型条件:对δ＞0及任意的方体Q, |Q|~(pα/n)‖u‖L(log L)~(2p-1+δ),Q(1/|Q|∫_Qv(x))-(p′/pdx)~(p/p′)≤K＜∞,则分数次积分算子I_α,0＜α＜n,是从L~p(v)到L~(p,∞)(u)的有界算子,1＜p＜∞．     

分数次积分在局部Hardy空间上的有界性质

证明了当0<αn/(n-α)时,分数次积分Iα是局部Hardy空间hp(Rn)到空间hp(Rn)+Lq(Rn)的一个线性映射.     

关于一个积分不等式的一些注记

Given two positive constantsαandβ,we prove that the integral inequality∫_0~1 f~(α+β)(x)dx≥∫_0~1 f~α(x)x~βdx holds for all non-negative valued continuous functions f satisfying∫_x~1 f(t)dt≥∫_x~1 tdt for x∈[0,1]if and only ifα+β≥1.This solves an open problem proposed recently by Ngo,Thang,Dat,and Tuan.     

用留数计算∫from x=-∞ to ∞ (R(x)e~(αix)dx)型积分注记

用留数计算积分∫from x=-∞ to ∞ (R(x)e~(αix)dx)(α>0)的方法可推广到α<0的情形,并举例计算一个函数的傅氏变换.     

用留数计算∫+∞-∞R(x)eαixdx型积分注记

用留数计算积分∫ ∞-∞R(x)eαixdx(α＞0)的方法可推广到α＜0的情形,并举例计算一个函数的傅氏变换.     

分数次积分交换子的一个端点估计

设0<β<1,α,β0<αnn-α.给出了当p=nn+β时,分数次积分I与L ipsch itz函数b的交换子从局部H ardy空间hp(Rn)到空间hp(Rn)+Lq(Rn)上的有界性估计.     

一些单叶函数族导数的积分平均值

K(α),st_k(α),C(β,α),(α<1,β<1)分别表示α阶凸函数族,k 次对称的α阶星形函数族,α型β阶的近于凸函数族.在这篇文章中,我们分別对(?)(K(α)的闭凸包),(?),(?),(α<1,β≤1/2)决定了凸泛函L(f)=(1/(2π)(?)))~(1/p),0≤r<1,p≥1,n=1,2,…,的极值和极值函数.我们的结果表明:极值函数仅依赖于函数族而与参数 n,r,p 无关;而且对任何固定的函数族,除掉旋转外极值函数是唯一的.     

Bochner-Martinelli型积分的边界性质

对 Cn中具光滑边界Ω的有界域 D和属于指数α( 0 <α <1 )的 Lipschitz空间 Lip(α,Ω )中的每个函数φ,我们不仅证明了 Bochner- Martinelli型积分Φ ( z) =∫Ωφ(ζ) K(ζ,z)(其中 K(ζ,z)为 Bochner- Martinelli型积分核 )表示的内、外极限值Φ +( t) ,Φ - ( t)属于 Lip(β,Ω ) ( 0 <β <α <1 )而且可分别延拓成 D和 Dc上的指数为β的 Holder连续函数 ,并由此给出了 Bochner- Martinelli变换的 Plemelj跳跃公式 .     

一类广义的Marcinkiewicz积分算子的有界性

研究了下述广义Marcinkiewicz积分算子μΩ,αf(x)=∫∞0|∫|x-y|≤tΩ(x-y)|x-y|n-1f(y)dy|2dtt3+2α12当零次齐次函数Ω∈Hq(Sn-1),q=n-1n-1+α,α≥0,且满足一定的消失性,则对于任意的1相似文献   

Weighted Integral Means of Mixed Areas and Lengths Under Holomorphic Mappings

This note addresses monotonic growths and logarithmic convexities of the weighted((1-t2)αdt2,-∞α∞,0t1)integral means Aα,β(f,)and Lα,β(f,)of the mixed area(πr2)-βA(f,r)and the mixed length(2πr)-βL(f,r)(0≤β≤1 and0r1)of f(rD)and f(rD)under a holomorphic map f from the unit disk D into the finite complex plane C.     

THE RISK MODEL OF THE EXPECTED DISCOUNTED PENALTY FUNCTION WITH CONSTANT INTEREST FORCE

In this article, the expected discounted penalty functionΦδ,α(u) with constant interest 5 and "discounted factor" exp(-αTδ) is considered. As a result, the integral equation ofΦδ,α(u) is derived and an exact solution forΦδ,α(0) is found. The relation between the joint density of the surplus immediately prior to ruin, and the deficit at ruin and the density of the surplus immediately prior to ruin is then obtained based on analytical methods.     

一类型集值积分方程解的存在性

本文设(X,)是Banach空间,L(X)是X的非空有界闭子集族,H是导出的Hausdorff度量.此外,∧是一指标集.作为准备,我们有以下Chen和Shin的结果对集值映象情形的推广: 引理设T_λ:X→L(X)(λ∈∧),使得这里函数φ满足(φ):φ:[0,∞)→[0,∞)不减,φ(t)0),且(?)α≥0,存在β>1及收敛序列{t_k}:t_0=0,t_1≥α,t_(k 1)=t_(k φ)(β(t_k-t_(k-1))(k=1,2,…),则存在     

沿齐次曲线的强奇异积分算子在调幅空间上的有界性

设Γ_θ(t)为R~n(n≥2)中的齐次曲线,定义沿齐次曲线的强奇异积分算子T_(n,α,β)f(x)=p.v.∫_(-1)~1f(x-Γ_θ(t))(e~((-2πi|t|)~(-β))/(t|t|~α))dt,α,β>0.本文讨论了上述奇异积分算子在广义调幅空间上的有界性.     

一类带弱奇异核非线性偏积分微分方程的全离散有限元

1引言我们将研究下面一类带弱奇异核非线性偏积分微分方程的数值解:u_t-▽·(a(u)▽u)-integral from n=0 to tβ(t-s)△u(s)ds=f(u),x∈Ω,t∈(?),(1.1) u(·,t)=0,x∈(?)Ω,t∈J,(1.2) u(·,0)=v(x),x∈Ω,(1.3)其中Ω为平面上的凸角域,J=(0,T],α和f为R上的光滑函数,满足0相似文献   

多线性分数次积分算子交换子的有界性

Ibαf ( x) =∫R ∏mj=1( bj( x) - bj( y) ) 1| x - y| n-αf ( y) dyare considered.The following priori estimates are proved.For 1 01Φ1t| {y∈Rn:| Ibαf( y) | >t}| 1q ≤csupt>01Φ1t| {y∈Rn:ML( log L) 1r ,α(‖b‖f ) ( y) >t}| 1q,where‖b‖=∏mj=1‖bj‖Oscexp Lrj,Φ( t) =t( 1 + log+t) 1r,1r =1r1+ ...+ 1rm,ML(…     

Toader型平均与几种经典平均的确界

给出了最佳参数α_1,α_2,α_3,β_1,β_2,β_3∈R,使得双向不等式α_1Q(a,b)+(1-α_1)G(a,b)0且a≠b成立.其中A(a,b)=(a+b)/2,H(a,b)=2ab/(a+b),G(a,b)=(ab)~(1/2),Q(a,b)=((a~2+b~2)/2)~(1/2),C(a,b)=(a~2+b~2)/(a+b),T(a,b)=2/π∫_0~(π/2)(a~2cos~2t+b~2sin~2)~(1/2)tdt分别是两个正数a和b的算术平均,调和平均,几何平均,二次平均,反调和平均和Toader平均.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

关于一个完全单调函数

设α>0和β是实数,则函数1+αxx+β在(0,∞)上是完全单调的充要条件是α≤2β.这推广了已有的结果.     

Weighted mean convergence of Hakopian interpolation on the disk

In this paper, we study weighted mean integral convergence of Hakopian interpolation on the unit disk D. We show that the inner product between Hakopian interpolation polynomial Hn(f;x,y) and a smooth function g(x,y) on D converges to that of f(x,y) and g(x,y) on D when n →∞, provided f(x,y) belongs to C(D) and all first partial derivatives of g(x,y) belong to the space LipαM(0 ＜α≤ 1). We further show that provided all second partial derivatives of g(x,y) also belong to the space LipαM and f(x,y) belongs to C1 (D), the inner product between the partial derivative of Hakopian interpolation polynomial (6)/(6)xHn(f;x,y) and g(x,y) on D converges to that between (6)/(6)xf(x,y) and g(x,y) on D when n →∞.