共查询到20条相似文献,搜索用时 31 毫秒
1.
Let Ta,φbe a Fourier integral operator defined by the oscillatory integral Ta,φu(x)=1/(2π)n∫Rn^eiφ(x,ξ)a(x,ξ)(u)(ξ)dξ,where a∈Se,δmandφ∈Φ2,satisfying the strong non-degenerate condition.It is shown that if0<(e)≤1,0≤δ<1 and m≤e2-n/2,thenTα,φis a bounded operator from L∞(Rn)to BMO(Rn). 相似文献
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设M是超有限Ⅱ1型因子.D是M的Cartan子代数,T是对角为D的M 的σ-弱闭的子代数(简称Cartan双模代数)并且生成M.设φ是T到T上的σ-弱连续满线性等距,则Φ可扩张成从M到M上的等距.设φ是T到T上的映射(没假设线性),满足任给a,b∈T,T上存在σ-弱连续满线性等距φa,b(与n,b有关),使得φa,b(a)=φ(a),φa,b(b)=φ(b),则φ是线性等距. 相似文献
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一类中立型高维周期微分系统的周期解 总被引:10,自引:1,他引:9
本文考虑中立型高维周期系统:其中(L,x)∈R×R~n,A(t,x)为连续函数矩阵,x_t∈C([-γ,0],R~n),x_t(θ)=x(t十θ),θ∈[-r,0],记C=C([-r,0],R~n),f:R×C→R~n连续,且A(t+T,X)=A(t,x),T,r>c∈R,本文用不动点方法研究此系统,得到了其周期解存在的充分性条件,所得结果推广、改进了文[1-3]中相应结论. 相似文献
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考虑约束最优化问题:minx∈Ωf(x)其中:f:R^n→R是连续可微函数,Ω是一闭凸集。本文研究了解决此问题的梯度投影方法,在步长的选取时采用了一种新的策略,在较弱的条件下,证明了梯度投影响方法的全局收敛性。 相似文献
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Given n ≥ 2 and a > 1/2,we obtained an improved upbound of Hausdorff's dimension of the fractional Schr(o)dinger operator; that is,sup f∈Hs(Rn) dimH{x∈Rn:limt→0... 相似文献
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利用重排的方法找到了H~p空间的一类函数,这类函数的H~p范数和Lp范数是等价的(0p≤1).对于每一个f∈L~p(R~n),存在一个函数g∈H~p(R~n)满足其分布函数相等d_f=d_g,并且||g||Lp≤||g||H~p≤Cp||g||Lp.另外,还介绍了一种构造H~p空间的L~∞-原子的方法. 相似文献
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This paper studies the behaviors of the solutions in the vicinity of a givenalmost periodic solution of the autonomous system
x′=f(x), x Rn , (1)
where f C1 (Rn ,Rn ). Since the periodic solutions of the autonomous system are not Liapunov asymptotic stable, we consider the weak orbitally stability.
For the planar autonomous systems (n=2), the classical result of orbitally stability about its periodic solution with period w belongs to Poincare, i.e. 相似文献
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强奇异卷积算子交换子的Hardy型空间估计 总被引:2,自引:0,他引:2
本文给出了强奇异卷积算子交换子[6,T]在Hardy型空间中的估计,其中 b∈BMO(Rn)且一致连续, T为强奇异卷积算子. 相似文献
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设函数b=(b1,b2,…,bm)和广义分数次积分L-a/2(0〈α〈n),它们生成多线性算子定义如下 Lb -a/2 f = [bm …, [b2[b1, L-a/2]],…, ]f,其中m ∈ Z+ , bi ∈ Lipβi (0 〈βi 〈 1),其中(1≤i≤m).将讨论Lb -1a/2。从Mp^q(Rn)到Lip(α+β-n/ q) ( Rn )和q^q ( Rn )到BMO(Rn)的有界性. 相似文献
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The authors investigate the influence of a harmonic potential and random perturbations on the nonlinear Schr(o)dinger equations.The local and global well-posedness are proved with values in the space ∑(Rn) ={f ∈ H1(Rn),| · |f ∈ L2(Rn)}.When the nonlinearity is focusing and L2-supercritical,the authors give sufficient conditions for the solutions to blow up in finite time for both confining and repulsive potential.Especially for the repulsive case,the solution to the deterministic equation with the initial data satisfying the stochastic blow-up condition will also blow up in finite time.Thus,compared with the deterministic equation for the repulsive case,the blow-up condition is stronger on average,and depends on the regularity of the noise.If φ =0,our results coincide with the ones for the deterministic equation. 相似文献
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Yi Zhou 《偏微分方程(英文版)》1997,10(1):19-30
In this paper, we continue to study the equation ◻Φ^I+f^I(Φ,∂Φ) = 0 where ◻ = -∂²_t + Δ denotes the standard D' Alembertian in R^{2+1} and the nonlinear terms f have the form f^I = Σ_{JK}Γ^I_{JK}(Φ)Q_0(Φ^J,Φ^K) with Q_0(Φ,φ) = -∂_tΦ∂_tφ + Σ&sup_{i=1}∂_iΦ∂_tφ and Γ^I_{JK} being C^∞ function of Φ. In Y. Zhou [1], we showed that the initial value problem Φ(0,x) = Φ_0(x), ∂_tΦ(0,x) = Φ_1 (x) is locally well posed for Φ_0 ∈ H^{s+1}, Φ_1 ∈ H^s with s = \frac{1}{8}. Here, we shall further prove that the initial value problem is locally well posed for any s > 0. 相似文献
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Pu Zhang Jiukun Hua 《分析论及其应用》2005,21(3):226-234
Let T be the multiplier operator associated to a multiplier m, and [b, T] be the commutator generated by T and a BMO function b. In this paper, the authors have proved that [b,T] is bounded from the Hardy space H^1(R^n) into the weak L^1 (R^n) space and from certain atomic Hardy space Hb^1 (R^n) into the Lebesgue space L^1 (R^n), when the multiplier m satisfies the conditions of Hoermander type. 相似文献
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一类奇异半线性热方程初值问题解 的唯一性结果 总被引:6,自引:0,他引:6
设u(t,x),u(t,x)为初值问题在带形域ST=(0,T)×Rn内的两个非负经曲解,f(x)连续有界非负的实函数,则有如下的结果:(1)若f(x)不恒为零,则在ST中u(t,x);(2)若γ>1,则在ST中u(t,x)u(t,x);(3)若0>γ>1,f(x)0,则问题(1.1),(1.2)的解不唯一且它的所有非平凡解的集合为u(t,s)=这里s≥0是参数,其中记号(γ)+=max{γ,0}. 相似文献
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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)。 相似文献
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文中讨论了振荡奇异积分:其中对满足一定凸性条件的P以及Ω∈L~q(S~(n-1))(q>1),证明了T在L~P(R~n)上有界,p>1. 相似文献
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张辉 《应用泛函分析学报》2000,2(1):26-33
研究了方程-div(‖Du‖^-2Du)=λf(u)在R^n,n≥2中环域上的正的径向解的多重性。当f在正区域上有多个峰的情况下,我们获得了多个解。 相似文献
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Let L be the infinitesimal generator of an analytic semigroup on L 2 (Rn)with Gaussian kernel bounds,and L-α/ 2 be the fractional integrals generated by L for 0< α 相似文献