共查询到20条相似文献,搜索用时 61 毫秒
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本文给出新Dirichlet级数Σ_(n=0)~∞a_ne~(λns)的收敛横坐标σ_c、一致收敛横坐标σ_u和绝对收敛横坐标σ_a的定义.通过指数λ_n和系数a_n的关系去估计三个横坐标,并补充证明两类Dirichlet级数Σ_(n=0)~∞a_ne~(λns)和Σ_(n=0)~∞a_ne~(-λns)的收敛条件是一致的. 相似文献
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《中国科学 数学(英文版)》2017,(8)
Let n 1 and Tm be the bilinear square Fourier multiplier operator associated with a symbol m,which is defined by Tm(f1, f2)(x) =(∫_0~∞︱∫_((Rn)2)e~(2πix·(ξ1+ξ2))m(tξ1, tξ2)?f1(ξ1)?f2(ξ2)dξ1dξ2︱~2(dt)/t) ~(1/2).Let s be an integer with s ∈ [n + 1, 2n] and p0 be a number satisfying 2n/s p0 2. Suppose that νω=∏_i~2=1ω_i~(p/pi) and each ω_i is a nonnegative function on Rn. In this paper, we show that under some condition on m, Tm is bounded from L~(p1)(ω_1) × L~(p2)(ω_2) to L~p(ν_ω) if p0 p1, p2 ∞ with 1/p = 1/p1 + 1/p2. Moreover,if p0 2n/s and p1 = p0 or p2 = p0, then Tm is bounded from L~(p1)(ω_1) × L~(p2)(ω_2) to L~(p,∞)(ν_ω). The weighted end-point L log L type estimate and strong estimate for the commutators of Tm are also given. These were done by considering the boundedness of some related multilinear square functions associated with mild regularity kernels and essentially improving some basic lemmas which have been used before. 相似文献
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选择搭配参数a,b,利用权函数方法可得Hilbert型级数不等式∞Σn=1∞Σm=1 K(m,n)ambn≤ M(a,b)||(a)||p,α(a,b)||(b)||q,β(a,b).该文讨论a,b应如何选取才能使具有拟齐次核的不等式中M(a,b)为最佳常数因子的问题,得到了a,b为最佳搭配参数的充分必要条件及最佳常数... 相似文献
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对任意正整数m,n,r,定义S_(n,m)~((r))=Σ_(k_1+K_2+…+k_m=n)(_(k_1,k_2,…,k_m)~n)~r,并定义T_(n,m)~((r))=Σ_(k_1+K_2+…+k_m=n)(-1)~(k_1)(_(k_1,k_2,…,k_m)~n)~r.对S_(n,m)~((r))和T_(n,m)~((r))获得了若干可除性性质. 相似文献
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设E是任意实Banach空间 ,K是E的非空闭凸子集· T :K→K是一致连续_半压缩映像且值域有界· 设 an ,bn ,cn ,a′n ,b′n 和 c′n 是 [0 ,1]中的序列且满足条件 :ⅰ )an bn cn =a′n b′n c′n =1, n≥ 0 ;ⅱ )limbn =limb′n =limc′n =0 ;ⅲ ) ∑∞n =0bn =∞ ;ⅳ )cn =o(bn) · 对任意给定的x0 ,u0 ,v0 ∈K ,定义Ishikawa迭代 xn 如下 : xn 1=anxn bnTyn cnun,yn =a′nxn b′nTxn c′nvn ( n≥ 0 ) ,其中un 和 vn 是K中两个有界序列· 则 xn 强收敛于T的唯一不动点· 最后研究了_强增殖算子方程解的Ishikawa迭代收敛性· 相似文献
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Let(ξ_n)_(n=0)~∞ be a Markov chain with the state space X = {1, 2, ···, b},(g_n(x, y))_(n=1)~∞ be functions defined on X × X, and F_(m_n,b_n)(ω) =1 /b_n sum from k=m_n+1 to m_n+b_n g_k(ξ_(k-1), ξ_k).In this paper the limit properties of F_(m_n,b_n)(ω) and the generalized relative entropy density f_(m_n,b_n)(ω) =-(1/b_n) log p(ξ_(m_n,m_n+b_n)) are discussed, and some theorems on a.s. convergence for(ξ_n)_n=0~∞ and the generalized Shannon-McMillan(AEP) theorem on finite nonhomogeneous Markov chains are obtained. 相似文献
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考虑[a,b](-∞<a<b<∞)上n阶复值系数正则对称微分算式ly=∑n j=0 aj(t)y(j).本文首先给出由lmy(m∈N且m≥2)生成的微分算子T(lm)自伴边条件一种新的描述,其次研究了由微分算式ly生成的m个微分算子Tk(l)(k=1,…,m)的积Tm(l)…T2(l)T1(l)的自伴性并获得其自伴的充分必要条件. 相似文献
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设E是具弱序列连续对偶映像自反Banach空间, C是E中闭凸集, T:C→ C是具非空不动点集F(T)的非扩张映像.给定u∈ C,对任意初值x0∈ C,实数列{αn}n∞=0,{βn}∞n=0∈ (0,1),满足如下条件:(i)sum from n=α to ∞α_n=∞, α_n→0;(ii)β_n∈[0,α) for some α∈(0,1);(iii)sun for n=α to ∞|α_(n-1) α_n|<∞,sum from n=α|β_(n-1)-β_n|<∞设{x_n}_(n_1)~∞是由下式定义的迭代序列:{y_n=β_nx_n (1-β_n)Tx_n x_(n 1)=α_nu (1-α_n)y_n Then {x_n}_(n=1)~∞则{x_n}_(n=1)~∞强收敛于T的某不动点. 相似文献
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Local Solvability for a Class of Nonhomogeneous Left Invariant Differential Operators on HR \bigotimes Rk 下载免费PDF全文
Fu Chuli 《偏微分方程(英文版)》1990,3(2):16-26
In this paper we discuss tbe local solvability of the following nonhomogeneous left invariant differential operators on the nilpotent Lie group H_n⊗R^K: P(X, Y, T, Z) = Σ_{|α+β|+ζ+|y|≤m|α+β|+2l=a}a_{αβly}X^αY^βT^lZ^y where X_j, Y_j (j = 1, 2, …, n), T, Z_j(j = l, 2, …, K) are bases of left invariant vector fields on H_n⊗R^K and a_{αβly} are complex constants. 相似文献
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Let Σ_1 and Σ_2 be m and n dimensional Riemannian manifolds of constant curvature respectively. We assume that w is a unit constant m-form in Σ_1 with respect to which Σ_0 is a graph. We set v = 〈e_1 ∧ … ∧ e_m, 〉), where {e_1, …, e_m} is a normal frame on Σ_t. Suppose that Σ_0 has bounded curvature. If v(x, 0) ≥ v0 > \frac{\sqrt{p}}{2} for all x, then the mean curvature flow has a global solution F under some suitable conditions on the curvatrue of Σ_1 and Σ_2. 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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令∑_p表示形如f(z)=z~(-p)+∑m=1∞(p∈N={1,2,3…})且在去心单位开圆盘D=U\{0}={z∶z∈C且0|z|1}上解析的亚纯多叶函数类.利用一个作用在∑_p上的乘积算子定义了几个新的亚纯函数的子类,并考虑这些函数类在积分算子作用下的性质. 相似文献
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Cauchy Problem for Semilinear Wave Equations in Four Space Dimensions with Small Initial Data 下载免费PDF全文
Yi Zhou 《偏微分方程(英文版)》1995,8(2):135-144
In this paper, we consider the Cauchy problem ◻u(t,x) = |u(t,x)|^p, (t,x) ∈ R^+ × R^4 t = 0 : u = φ(x), u_t = ψ(x), x ∈ R^4 where ◻ = ∂²_t - Σ^4_{i=1}∂²_x_i, is the wave operator, φ, ψ ∈ C^∞_0 (R^4). We prove that for p > 2 the problem has a global solution provided tile initial data is sufficiently small. 相似文献
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This paper studies the initial-boundary value problem of GBBM equations u_t - Δu_t = div f(u) \qquad\qquad\qquad(a) u(x, 0) = u_0(x)\qquad\qquad\qquad(b) u |∂Ω = 0 \qquad\qquad\qquad(c) in arbitrary dimensions, Ω ⊂ R^n. Suppose that. f(s) ∈ C¹ and |f'(s)| ≤ C (1+|s|^ϒ), 0 ≤ ϒ ≤ \frac{2}{n-2} if n ≥ 3, 0 ≤ ϒ < ∞ if n = 2, u_0 (x) ∈ W^{2⋅p}(Ω) ∩ W^{1⋅p}_0(Ω) (2 ≤ p < ∞), then ∀T > 0 there exists a unique global W^{2⋅p} solution u ∈ W^{1,∞}(0, T; W{2⋅p}(Ω)∩ W^{1⋅p}_0(Ω)), so the known results are generalized and improved essentially. 相似文献
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Bang-He Li 《数学研究》2016,49(4):319-324
Let $ζ(s)$ be the Riemann zeta function, $s=\sigma+it$. For $0 < \sigma < 1$, we expand $ζ(s)$ as the following series convergent in the space of slowly increasing distributions
with variable $t$ : $$ζ(\sigma+it)=\sum\limits^∞_{n=0}a_n(\sigma)ψ_n(t),$$ where $$ψ_n(t)=(2^nn!\sqrt{\pi})^{-1 ⁄ 2}e^{\frac{-t^2}{2}}H_n(t),$$ $H_n(t)$ is the Hermite polynomial, and $$a_n(σ)=2\pi(-1)^{n+1}ψ_n(i(1-σ))+(-i)^n\sqrt{2\pi}\sum\limits^∞_{m=1}\frac{1}{m^σ}ψ_n(1nm).$$ This paper is concerned with the convergence of the above series for $σ > 0.$ In the deduction,
it is crucial to regard the zeta function as Fourier transfomations of Schwartz'
distributions. 相似文献
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In this paper we study the initial boundary value problem of GBBM equations on unbounded domain u_t - Δu_t = div f(u) u(x,0) = u_0(x) u|_{∂Ω} = 0 and corresponding Cauchy problem. Under the conditions: f( s) ∈ C^sup1 and satisfies (H)\qquad |f'(s)| ≤ C|s|^ϒ, 0 ≤ ϒ ≤ \frac{2}{n-2} if n ≥ 3; 0 ≤ ϒ < ∞ if n = 2 u_0(x) ∈ W^{2,p}(Ω) ∩ W^{2,2}(Ω) ∩ W^{1,p}_0(Ω)(W^{2,p}(R^n) ∩ W^{2,2}(R^n) for Cauchy problem), 2 ≤ p < ∞, we obtain the existence and uniqueness of global solution u(x, t) ∈ W^{1,∞}(0, T; W^{2,p}(Ω) ∩ W^{2,2}(Ω) ∩ W^{1,p}_0(Ω))(W^{1,∞}(0, T; W^{2,p}(R^n) ∩ W^{2,2} (R^n)) for Cauchy problem), so the results of [1] and [2] are generalized and improved in essential. 相似文献