共查询到20条相似文献,搜索用时 15 毫秒
1.
张传洲 《应用泛函分析学报》2008,10(3):228-233
对维林金系统{ψ,n≥1}和0<α< 1定义极大算子σ^α*f:= sup │σ^αnf│,其中σ^αnf是函数f的(C,α)平均值.证明了算子σ^α*是(p,p)型(1〈P〈∞)和弱(1,1)型.另外‖σ^α*f‖1≤C‖f‖H1,,其中H1是Hardy空间.利用上述结果,证明了对任一可积函数f,σ^αnf几乎处处收敛于f. 相似文献
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讨论了在q=2的情形下,Littlewood-Paley gλ*函数在加权Herz型Hardy空间中的有界性,即当0
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关于广义Aluthge变换的谱性质的研究 总被引:2,自引:0,他引:2
设T∈H(H),T=U|T|是算子T的极分解,则定义T^λ=|T|^λU|T|^1-λ和T^λ(*)=|T*|^λU|T*|^1-λ,(其中0〈λ〈1)分别为算子的广义Aluthge变换和广义*-Aluthge变换.本文中主要研究了三者之间的几种谱的关系.同时,还证明了算子T满足修正的Weyl定理当且仅当弘满足修正的Weyl定理当且仅当T^λ(*)满足修正的Weyl定理.最后证明了算子T满足a—Weyl定理当且仅当T^λ满足a—Weyl定理. 相似文献
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在Qp空间上建立了Jackson型不等式,即对任意f(z)=∑j=0 ^∞ αjz^j∈Qp,0≤p〈∞,α〉1及k-1∈N,有
||f(z)-Г(k)/Г(k+α)∑ j=0 ^k-1Г(k-j+α)/Г(k-j)αjz^j||Qp≤C(α)ω(1/k,f,Qp),其中ω(1/k,f,Qp)为Qp空间中的连续模,C(α)是仅与参数α有关的正常数. 相似文献
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定理 设数列{αn}是等差数列,sn=α1^m+α2^m+…+αn^m,m∈N^*,则存在λi∈R(i=2,3,…,m+1),有g(n)=λm+1αn^m+1+λmαn^m+…+λ3αn^3+λ2αn^2,使{sn-g(n)}为等差数列. 相似文献
7.
Ana Bela CRUZEIRO Xi Cheng ZHANG 《数学学报(英文版)》2006,22(1):101-104
For 1 〈 p ≤2, an L^p-gradient estimate for a symmetric Markov semigroup is derived in a general framework, i.e. ‖Γ^/2(Ttf)‖p≤Cp/√t‖p, where F is a carre du champ operator. As a simple application we prove that F1/2((I- L) ^-α) is a bounded operator from L^p to L^v provided that 1 〈 p 〈 2 and 1/2〈α〈1. For any 1 〈 p 〈 2, q 〉 2 and 1/2 〈α 〈 1, there exist two positive constants cq,α,Cp,α such that ‖Df‖p≤ Cp,α‖(I - L)^αf‖p,Cq,α(I-L)^(1-α)‖Df‖q+‖f‖q, where D is the Malliavin gradient ([2]) and L the Ornstein-Uhlenbeck operator. 相似文献
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讨论边值问题((一v'(r))~n)'=λ(v~α+v~β),v'(0)=v(1)=0,其中λ〉0是正参数.对(n-α)(n-β)〉0的情形得出了正解的存在唯一性.对0〈α〈n〈β的情形得到,存在λ~*〉0,使得当0〈λ〈λ~*时,此边值问题恰好存在两个正解;当λ=λ~*时,此边值问题存在唯一一个正解;当λ〉λ~*时,此边值问题不存在正解. 相似文献
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B. FISHER K. TAS 《数学学报(英文版)》2006,22(6):1639-1644
Let f and g be distributions and let gn = (g * δn)(x), where δn (x) is a certain converging to the Dirac delta function. The non-commutative neutrix product fog of f and g to be the limit of the sequence {fgn }, provided its limit h exists in the sense that sequence is defined N-lim n-∞(f(x)g,, (x), φ(x)〉 = (h(x), φ(x)},for all functions p in 2. It is proved that (x^λ+1n^px+)0(x^μ+1n^qx+)=x+^λμ1n^p+qx+,(x^λ-1n^qx-)=x-^λ+μ1n^p+qx-,for λ+μ〈-1; λ,μ, λ+μ≠-1,-2…and p,q=0,1,2…… 相似文献
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Pu Zhang 《数学学报(英文版)》2008,24(8):1387-1400
Let μ be the n-dimensional Marcinkiewicz integral and μb the multilinear commutator of μ. In this paper, the following weighted inequalities are proved for ω ∈ A∞ and 0 〈 p 〈 ∞,
||μ(f)||LP(ω)≤C|Mf|LP(ω) and ||μb(f)||LP(ω)≤C||ML(log L)^1/r f||LP(ω).
The weighted weak L(log L)^1/r -type estimate is also established when p=1 and ω∈A1. 相似文献
||μ(f)||LP(ω)≤C|Mf|LP(ω) and ||μb(f)||LP(ω)≤C||ML(log L)^1/r f||LP(ω).
The weighted weak L(log L)^1/r -type estimate is also established when p=1 and ω∈A1. 相似文献
12.
R~N上临界增长的椭圆方程无穷多解的存在性 总被引:3,自引:0,他引:3
本文证明了RN上的拟线性椭圆型方程-div(|Du|p-2Du)+|u|p-2u=λ(x)·|u|α-2u+a(x)|u|s-2u+b(x)|u|p*-2u在W1,p(RN)中无穷多解的存在性,其中N≥3,2≤p相似文献
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加权Herz型Hardy空间上的Littlewood-Paley g函数 总被引:2,自引:0,他引:2
王月山 《纯粹数学与应用数学》2001,17(3):220-226
研究了Littlewood-Paley g函数gψ(f)(x)在加权Herz型Hardy空间上的性质,得到了如下结果,若ω1,ω2∈A1,则当n(1-1/q)≤α≤n(1-1/q) ε时,gψ为HK^a,p q(ω1,ω2)到K^a,p q(ω1,ω2)上的有界算子,当α=n(1-1/) ω时,gψ为HK^a,p q(ω1,ω2)到WK^a,p q(ω1,ω2)上的有界算子。 相似文献
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设1〈P≤2,0〈n≤1,X是P一致可光滑空间的Banach空间,则对每个X值拟鞅f=(fn)n≥0∈pHn^σ(X)存在分解fn=∑k∈Zμkαn^k(n≥0),并且||f||pHα^σ(X)+||R(f)||α~inf(∑k∈μk^a)^1/a,这里a^k=(an^k)n≥(k∈Z)是一列(1,α,∞;p)拟鞅原子,并且在L^1中收敛,sup k∈z||a^k*||n〈∞,(μk)k∈Z∈la是非负实数列.对于拟鞅空间pHa^s(X)和qKn(x)成立类似的结果.此外,利用拟鞅原子分解定理,证明了几个拟鞅不等式. 相似文献
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Joseph A. Iaia 《偏微分方程(英文版)》2010,(1):33-67
We study capillary spreadings of thin films of liquids of power-law rheology. These satisfy ut+(u^λ+2|uxxx|^λ-1uxxx)x=0,where u (x, t) represents the thickness of the one-dimensional liquid and λ 〉 1. We look for traveling wave solutions so that u(x,t) =g(x+ct) and thus g satisfies g'''=|g-ε|^1/λ/g^1+2/λ sgn(g-ε) We show that for each ε 〉 0 there is an infinitely oscillating solution, gε, such that limt→∞ gε=ε and that gε→ g0 as ε → O, where g0≡ 0 for t ≥ 0 and g0=cλ|t|3λ/2λ+1 for t〈0 for some constant cλ. 相似文献
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本文讨论了下面一类带,Hardy项和临界非线性项的半线性椭圆问题:{-△u-μ u/|x|^2+a(x)u=|u|^2^*-2 u+k(x)|u|^q-2u,u∈H^1(R^N)(*)的全局紧性结果及其正解的存在性,其中2^*=2N/(N-2)是临界的Sobolev指标,2〈q〈2^*,0≤μ〈μ^-△=(N-2)^2/4,a(x),k(x)∈C(R^N).通过对问题(*)所对应的能量泛函进行紧性分析,在a(x)和k(x)满足一定条件下,得到了此问题正解的存在性. 相似文献
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E. M. E. ZAYED 《数学学报(英文版)》2005,21(4):733-752
The trace of the wave kernel μ(t) =∑ω=1^∞ exp(-itEω^1/2), where {Eω}ω^∞=1 are the eigenvalues of the negative Laplacian -△↓2 = -∑k^3=1 (δ/δxk)^2 in the (x^1, x^2, x^3)-space, is studied for a variety of bounded domains, where -∞ 〈 t 〈 ∞ and i= √-1. The dependence of μ (t) on the connectivity of bounded domains and the Dirichlet, Neumann and Robin boundary conditions are analyzed. Particular attention is given for a multi-connected vibrating membrane Ω in Ra surrounded by simply connected bounded domains Ω j with smooth bounding surfaces S j (j = 1,……, n), where a finite number of piecewise smooth Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth components Si^* (i = 1 + kj-1,……, kj) of the bounding surfaces S j are considered, such that S j = Ui-1+kj-1^kj Si^*, where k0=0. The basic problem is to extract information on the geometry Ω by using the wave equation approach from a complete knowledge of its eigenvalues. Some geometrical quantities of Ω (e.g. the volume, the surface area, the mean curvuture and the Gaussian curvature) are determined from the asymptotic expansion ofexpansion of μ(t) for small │t│. 相似文献
18.
Jing YANG Shi Xin LUO Ke Qin FENG 《数学学报(英文版)》2006,22(3):833-844
Assume that m ≥ 2, p is a prime number, (m,p(p - 1)) = 1,-1 not belong to 〈p〉 belong to (Z/mZ)^* and [(Z/mZ)^*:〈p〉]=4.In this paper, we calculate the value of Gauss sum G(X)=∑x∈F^*x(x)ζp^T(x) over Fq,where q=p^f,f=φ(m)/4,x is a multiplicative character of Fq and T is the trace map from Fq to Fp.Under our assumptions,G(x) belongs to the decomposition field K of p in Q(ζm) and K is an imaginary quartic abelian unmber field.When the Galois group Gal(K/Q) is cyclic,we have studied this cyclic case in anotyer paper:"Gauss sums of index four:(1)cyclic case"(accepted by Acta Mathematica Sinica,2003).In this paper we deal with the non-cyclic case. 相似文献
19.
Let Ω IR^N, (N ≥ 2) be a bounded smooth domain, p is Holder continuous on Ω^-,
1 〈 p^- := inf pΩ(x) ≤ p+ = supp(x) Ω〈∞,
and f:Ω^-× IR be a C^1 function with f(x,s) ≥ 0, V (x,s) ∈Ω × R^+ and sup ∈Ωf(x,s) ≤ C(1+s)^q(x), Vs∈IR^+,Vx∈Ω for some 0〈q(x) ∈C(Ω^-) satisfying 1 〈p(x) 〈q(x) ≤p^* (x) -1, Vx ∈Ω ^- and 1 〈 p^- ≤ p^+ ≤ q- ≤ q+. As usual, p* (x) = Np(x)/N-p(x) if p(x) 〈 N and p^* (x) = ∞- if p(x) if p(x) 〉 N. Consider the functional I: W0^1,p(x) (Ω) →IR defined as
I(u) def= ∫Ω1/p(x)|△|^p(x)dx-∫ΩF(x,u^+)dx,Vu∈W0^1,p(x)(Ω),
where F (x, u) = ∫0^s f (x,s) ds. Theorem 1.1 proves that if u0 ∈ C^1 (Ω^-) is a local minimum of I in the C1 (Ω^-) ∩C0 (Ω^-)) topology, then it is also a local minimum in W0^1,p(x) (Ω)) topology. This result is useful for proving multiple solutions to the associated Euler-lagrange equation (P) defined below. 相似文献
1 〈 p^- := inf pΩ(x) ≤ p+ = supp(x) Ω〈∞,
and f:Ω^-× IR be a C^1 function with f(x,s) ≥ 0, V (x,s) ∈Ω × R^+ and sup ∈Ωf(x,s) ≤ C(1+s)^q(x), Vs∈IR^+,Vx∈Ω for some 0〈q(x) ∈C(Ω^-) satisfying 1 〈p(x) 〈q(x) ≤p^* (x) -1, Vx ∈Ω ^- and 1 〈 p^- ≤ p^+ ≤ q- ≤ q+. As usual, p* (x) = Np(x)/N-p(x) if p(x) 〈 N and p^* (x) = ∞- if p(x) if p(x) 〉 N. Consider the functional I: W0^1,p(x) (Ω) →IR defined as
I(u) def= ∫Ω1/p(x)|△|^p(x)dx-∫ΩF(x,u^+)dx,Vu∈W0^1,p(x)(Ω),
where F (x, u) = ∫0^s f (x,s) ds. Theorem 1.1 proves that if u0 ∈ C^1 (Ω^-) is a local minimum of I in the C1 (Ω^-) ∩C0 (Ω^-)) topology, then it is also a local minimum in W0^1,p(x) (Ω)) topology. This result is useful for proving multiple solutions to the associated Euler-lagrange equation (P) defined below. 相似文献
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研究了下列Henon方程解的渐近性态:-△u=|x|^αu^p-1,u〉0,x∈B1(0)∪→R(n≥3),u=0,x∈δB1(0).这里α〉0,p从左边趋近于p(α)=2(n+α)/n-1〉2n/n-2(n≥3). 相似文献