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1.
In this paper, we prove an extrapolation theorem of operators in martingale spaces with A
p
weights, which shows that for operators T defined on martingale space L
u
1
, if T is bounded on martingale space L
p0(w) for some 1 < p
0 < ∞ and every, w∈ A
∞, so it is on L
p,s
(w) for every 1 < p, s < ∞, and w ∈ A
∞. We also get some properties of A
p
weights and prove that if w ∈ A
1, then the maximal operator M is bounded on L
p,q
(w) with 1 < p < ∞, 1 < q ≤ ∞. 相似文献
2.
Holub proved that any bounded linear operator T or -T defined on Banach space L 1(μ) satisfies Daugavet equation1+‖T‖=Max{‖I+T‖, ‖I-T‖}.Holub's theorem is generalized to the nonlinear case: any nonlinear Lipschitz operator f defined on Banach space l 1 satisfies1+L(f)=Max{L(I+f), L(I-f)},where L(f) is the Lipschitz constant of f. The generalized Holub theorem has important applications in characterizing the invertibility of nonlinear operator. 相似文献
3.
The principles of the new maximal operator H* we defined are discussed. We prove that it is bounded from martingale Hardy-Lorentz L^Xp.q[0,1) to the Lorentz L^Xp.q[0,1) for 1/2〈 p〈∞, 0〈~ q ≤ ∞, where X is any Banach space. When the Banach space X has the RN property, the sequence dnHnf converges to f a.e. Meanwhile the convergence in L^Xp norm for 1≤p〈∞ is a consequence of that the family functions K (n∈N) is an approximate identity. 相似文献
4.
杨奇祥 《吉林大学学报(理学版)》2002,40(4):331-338
对于只满足Hormander条件的C-Z算子,在不假设其在L2上连续,
也不假设其共轭算子的性质,只假设T把特征原子映到WL1空间的条件下,有对任意1<p<∞,
T: Lp→Lp连续. 相似文献
5.
It is well known that, the singular integral operatorS defined as:
ifL is a closed smooth contour in the complex plane C, thenS is a bounded linear operator fromH
μ(L) intoH
μ(L): ifL is an open smooth curve, thenS is just a linear operator fromH
* intoH
*. In this paper, we define a Banach space
, and prove that
is a bounded linear operator, then verify the boundedness of other kinds of singular integral operators.
Supported by the National Science Foundation of China
Wang Xiaolin: born in Aug. 1950, Professor 相似文献
6.
研究了下面带有p-Laplacian算子的非线性奇异边值系统:(фp(u'i))'+ai(t)fi(u1,u2)=0, 0<t<1,αiфp(ui(0))-βiфp(u'i(0))=0, γiфp(ui(1))+δiфp(u'i(1))=0,(i=1,2)正解的存在性。其中фp(s)为p-Laplacian 算子,即фp(s)=|s|p-2s, p>1, (фp)-1=фq,1/p+1/q=1, αi>0, βi≥0, γi>0, δi≥0, i=1,2.这里fi是下半连续函数(i=1,2). 通过使用锥上的不动点定理,在相当弱的条件下, 获得了这类奇异边值系统正解的存在性. 相似文献
7.
证明了在二维小波子空间上存在一种傅立叶对偶算法,即由φ生成的二维小波子空间V0是L2(0,1)2到L2(R2)的有界可逆线性算子T的值域. 通过T扩展L2((0,1)2)空间的Riesz基,进而得到V0∈L2(R2)空间的采样定理. 相似文献
8.
非线性椭圆边值问题解的存在性 总被引:1,自引:0,他引:1
魏利 《吉首大学学报(自然科学版)》2000,21(3):42-44
利用含伪单调算子的变分不等式的解的存在性定理, 研究了一类与P拉普拉斯算子相关的非线性椭圆边值问题在 Lp(Ω , 2≤p < + ∞空间中解的存在性. 相似文献
9.
Let dμ=ϕdν be a complex valued measure where ν is a non-negative measure and ϕ is a complex valued function which satisfiesb
p
+
orb
∞
+
⊂a
1 condition. We prove some basic martingale inequalities such as B-G inequalities, weak (p, p) and strong (p, p) type inequalities for Banach space valued martingale with respect to complex measure μ.
Supported by the National Natural Science Foundation of China
Hou Youliang: born in 1956, Ph. D 相似文献
10.
It is dealt with positive solutions to the systems: u-t-u- XX =v+p, v-t-v XX =u+q in Ω×(0, T) subject to either initial conditions or boundary_value conditions. The exact blowup rate estimates of solution are established under some monotonicity assumptions on the initial values. 相似文献
11.
Let γ(t) be an even function extended by the evil ladder (tri-adic Cantor function) γ(t). Denote the curve Γ(t)= (t,γ(t)) ( -1≤t≤1). It is shown that the Hilbert transform along this curve Γ is bounded on L2 (R2). 相似文献
12.
线性交换子的加权估计 总被引:2,自引:2,他引:0
多线性交换子Tb(f)(x)=∫Rn∏i=1m(bi(x)-bi(y))k(x,y)f(y)dy在Lp(Rn)(1
K是一个标准的Calderón-Zygmund核.主要研究交换子Mf(x)=supx∈Q∫Q|f(y)|dy,其中f∈Lloc(Rn),x∈Rn,Q是任何包含x的方体,并用Sharp极大估计得到了该多线性交换子在Herz空间的一个加权有界性. 相似文献
13.
Let φ be a holomorphic self-map of the open unit polydisk U nin C nand ψ a holomorphic function on U n,p,q0. ∨In this paper,we study the generally weighted Bloch space. The growth estimation of functions in such a kind of space is given by the use of the integral method. Using the growth estimation of functions and the function-theoretical properties of those maps ψ and φ,sufficient conditions for the weighted composition operator Wψ,φ induced by ψ and φ to be bounded and compact between the generally weighted Bloch spaces are investigated. 相似文献
14.
构造了一类积分型插值,在连续函数空间和L_p空间内研究插值逼近方法的基础上,利用函数逼近论中的常用方法和技巧以及连续模、Holder不等式、Markov不等式等工具得到了该插值在Orlicz空间内的逼近定理。由于Orlicz空间包含连续函数空间和L_p空间,其拓扑结构也比连续函数空间和L_p空间复杂得多,且该类插值在基础研究和工程领域中有着非常重要的应用,所以论文的结果具有一定的拓展意义。 相似文献
15.
Introduction Many (1 1)-dimensional integrable systems can be re- duced from the Kadomtsev-Petviashvili (KP) hierarchy, with the most typical examples including the Gelfand- Dickey hierarchy (N-Korteweg de Vries (KdV) hierar- chy)[1] and the so called con… 相似文献
16.
17.
分别测定在有超声波作用和在无超声波作用条件下 ,酸化碘酸钾 (KIO3 )和亚硫酸钠 (Na2 SO3 )反应的反应速率方程式及活化能 ,从而研究该反应的机理以及超声波在该反应中的作用 ,并确定反应的最佳条件。实验得出 ,超声波对该反应有一定的促进作用 ,但是这种促进作用只提高反应的速率常数和降低反应的活化能 ,并没有改变反应机理。在超声波功率为 30 0W时 ,反应的速率方程表示式为 :v =k·c1 0 9(KIO3 ) ·c1 0 0 (Na2 SO3 )·c1 0 8(H+ ) ,其中 :k =95 0 (mol-1·L) 2 ·s-1,活化能为 17 35kJ·mol-1。实验还得出 ,在温度为2 98K时 ,当KIO3 与Na2 SO3 的初始浓度比为 2∶5 ,H+ 的初始浓度为 0 0 4 2 8mol·L-1,超声功率为 30 0W时 ,反应速率为最快 ,即v =4 31× 10 -4mol·L-1·s-1)。 相似文献
18.
The explicit common eigenvectors for complex scalar fields φ (x) and φ+ (x) are derived . They span an orthonormal and complete space. Based on this, the charge conjugate unitary operator and the operator which generates Bogolyubov pseudo-particles transformation can be neatly derived. It is emphasized that | ξ> is different from the direct product of two independent eigenvectors respectively belonging to two real scalar fields, and | ξ > is named the correlated eigenstates of φ( x) and φ+ (x). 相似文献
19.
We study the number of k-cycles in a random graph G(n, p). We estimate the probability that a random graph contains more k-cycles than expected. In this case, the usual martingale inequality with bounded difference is not effective. By constructing
a variable that approximates to the number of k-cycles in a random graph and using a new and extensive martingale inequality, we get the results in this paper.
Foundation item: Supported by the National Natural Science Foundation of China (10571139) 相似文献
20.
Optimal representation of multivariate functions or data in visualizable low-dimensional spaces 总被引:1,自引:0,他引:1
Jian Song 《科学通报(英文版)》2001,46(16):1337-1345
It is intended to find the best representation of high-dimensional functions or multivariate data in L2(Ω ) with fewest number of terms, each of them is a combination of one-variable function. A system of nonlinear integral equations has been derived as an eigenvalue problem of gradient operator in the said space. It proved that the complete set of eigenfunctions generated by the gradient operator constitutes an orthonormal system, and any function of L2(Ω ) can be expanded with fewest terms and exponential rapidity of convergence. It is also proved as a corollary, the greatest eigenvalue of the integral operators has multiplicity 1 if the dimension of the underlying space Rn, n = 2, 4 and 6. 相似文献