共查询到20条相似文献,搜索用时 359 毫秒
1.
2.
《数学物理学报(A辑)》2020,(1)
令(M~n,g)为n维无边紧黎曼流形,0αn,qn/n-α,该文研究了下列HardyLittlewood-Sobolev (HLS)不等式‖I_αf‖_L~q(M~n)≤C‖f‖L~p(M~n),■的极值问题.首先,利用算子I_α:L~p(M~n)→L~q(M~n)在次临界情形(即p(nq)/(n+αq))时的紧致性,证明p(nq)/(n+αq)时极值函数f_p∈L~p(M~n)的存在性;进而证明函数列{f_p}为临界情形时HLS不等式的最佳常数的极值列;最后,结合极值列{f_p}在L((nq)/(n+αq))(M~n)中的一致有界性,利用文献[32]建立的集中列紧原理证明{f_p}在L((nq)/(n+αq))(M~n)中存在收敛子列,从而给出临界情形(即p=((nq)/(n+αq)))时极值函数的存在性. 相似文献
3.
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
4.
本文主要研究了Cn单位球上Hilbert值Dμ,q函数的收敛性,得到了若f=∑α≥0xαzα∈Dμ,q,q>(2n)/(μ),则φ(z)=∑α≥0‖xα‖zα∈Lipγ,其中0<μ<1(n=1)或0<μ<2(n>1).此外还得到若f∈Dμ,q,q>(2n)/(μ),则对几乎所有的{εα}有fω(z)∈H∞,其中0<μ<1(n=1)或0<μ<2(n>1).在此过程中,我们利用了Banach空间几何学和Rademacher函数序列的知识. 相似文献
5.
最近,孙华定义了一类新的精细化Eulerian多项式,即$$A_n(p,q)=\sum_{\pi\in \mathfrak{S}_n}p^{{\rm odes}(\pi)}q^{{\rm edes}(\pi)},\ \ n\ge 1,$$ 其中$S_n$表示$\{1,2,\ldots,n\}$上全体$n$阶排列的集合, odes$(\pi)$与edes$(\pi)$分别表示$S_n$中排列$\pi$的奇数位与偶数位上降位数的个数.本文利用经典的Eulerian多项式$A_n(q)$ 与Catalan 序列的生成函数$C(q)$,得到精细化Eulerian 多项式$A_n(p,q)$的指数型生成函数及$A_n(p,q)$的显示表达式.在一些特殊情形,本文建立了$A_n(p,q)$与$A_n(0,q)$或$A_n(p,0)$之间的联系,并利用Eulerian数表示多项式$A_n(0,q)$的系数.特别地,这些联系揭示了Euler数$E_n$与Eulerian数$A_{n,k}$之间的一种新的关系. 相似文献
6.
《应用泛函分析学报》2017,(3)
本文研究参数边界条件下Sturm-Liouville算子的逆谱问题.利用Weyl函数的结果,证明对固定的n,n∈N_0,及不同的b_k,谱集合{λ_n(q,b_k)}_(k=1)~(+∞)能够唯一确定[0,1]上的势函数q(x),这个定理是文献[4]结果的本质推广. 相似文献
7.
众所周知,复合算子问题是函数空间的一个基本问题.就一般情形而言,依赖导数刻画的全纯函数空间其复合算子问题要比单复变时复杂.本文讨论了高维单位球上边界一般函数空间Fp,q,s(B)到Bloch型空间B~((q+n)/p)(B)复合算子有界或紧的充要条件问题,尤其给出了p≠q+n时紧性的简洁充要条件. 相似文献
8.
利用复函数的Euler公式,给出了函数项级数n=1∑∞cosnx/qn(q〉1)和n=1∑∞sinnx/qn(q〉1)的和函数表达式,该结果是[1]的推广. 相似文献
9.
本文研究了广义Euler函数的计算公式.利用初等的方法和技巧,给出了两类特殊广义Euler函数的准确计算公式,即φ_(pq)(n)以及φ_e(n)(e=p, p~2),其中n的任意素因数m≡1或者-1(mod e)且gcd(m, e)=1, p, q是不同的素数.这些结果是文献[5]相应结果的直接推广. 相似文献
10.
本文采用一簇新的核函数设计原始-对偶内点算法用于解决P*(κ)线性互补问题.通过利用一些优良、简洁的分析工具,证明该算法具有O(q(2κ+1)n1/p(logn)1+1/qlog(n/ε))迭代复杂性. 相似文献
11.
12.
Kunyang Wang Feng Dai 《分析论及其应用》2007,23(1):50-63
As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years (2001-2005). The main topics are: convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths. 相似文献
13.
We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals. 相似文献
14.
Yuxian Zheng 《分析论及其应用》2006,22(2):136-140
In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p(R^n) into the Lebesgue space L^p with p 〈 1. 相似文献
15.
H. H. Cuenya M.D. Lorenzo C. N. Rodriguez 《分析论及其应用》2007,23(2):162-170
In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms. 相似文献
16.
ZHENG ShiJun 《分析论及其应用》2004,20(3)
Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V. 相似文献
17.
It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary. 相似文献
18.
《计算数学》2014,(2)
<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists 相似文献
19.
20.
《中国科学 数学(英文版)》2014,(8)
<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by 相似文献