共查询到20条相似文献,搜索用时 62 毫秒
1.
本文给出空间退化的弱(L1,L2)-BLD映射的定义.利用Hodge分解,弱逆Holder不等式等工具,证明了其正则性结果对任意满足0<L2lnl/2l2n+l×100n2[23l/2.(24l+n+1)](l-q1)<1的q1,都存在可积指数p1=p1(n,l,q1,L1,L2)>l,使得对任意退化的弱(L1,L2)-BLD映射f∈W1,q1
loc(Ω,Rn),都有f∈W1,p1 loc (Ω,Rn),即f为通常意义下的退化的(L1,L2)-BLD映射. 相似文献
2.
本文给出空间退化的弱(L1,L2)-BLD映射的定义.利用Hodge分解,弱逆Holder不等式等工具,证明了其正则性结果:对任意满足Ol,使得对任意退化的弱(L1,L2)-BLD映射f∈Wloc1,q1(Ω,Rn),都有f∈Wloc1,p1(Ω,Rn),即f为通常意义下的退化的(L1,L2)-BLD映射. 相似文献
3.
本文首先将文[1]中的BLD映射推广为弱(L1,L2)-BLD映射,并证明了如下正则性结果:存在两个可积指数 P1=P1(n,L1,L2)<n<q1=q1(n,L1,L2),使得对任意弱(L1,L2)-BLD映射f∈(Ω,Rn),都有f∈(Ω,Rn),即f为(L1,L2)-BLD映射. 相似文献
4.
对于低于自然可积指数Sobolev类Wloc1,p(Ω,Rn)(1<p<n)的弱拟正则映射,建立了其广义微商可积指数提高到大于空间维数n结果,从而得出拟正则映射的可去奇异集的Hausdorff维数大于零的结论.本文是从弱拟正则映射定义出发对Iwaniec的有关结果给出一个简化证明. 相似文献
5.
关于图的L(2,1)标号核图 总被引:3,自引:0,他引:3
图的L(2,1)标号核图来自频率分配问题而导致的图论问题.在本文中,我们证得(i)对任意简单图G,存在G的一个标号核图Gcore,使得L(G)=L(Gcore)和L(G)≥|V(Gcore)|-1;(ii)设图G有p个顶点且边集|E(G)|≠φ,存在路
Pi G(1≤i≤m)和路Hs G(1≤s≤n),其中在G中V(Pi)∩V(Pj)=φ(i≠j),在G中V(P,)∩V(Pt)=φ(s≠t),则有m∑t=1|V(Pt)|+n∑s=1|V(Hs)|-(m+n)≥p;(iii)G是p(p≥5)个顶点的简单图,则有p+3≤L(G)+L(G)≤3p-4. 相似文献
6.
Hung Viet LE 《数学物理学报(B辑英文版)》2014,(4):1331-1344
Let h be a measurable function defined on R+×R+. LetΩ∈ L(log L+)νq(Sn1-1×Sn2-1)(1 ≤νq≤ 2) be homogeneous of degree zero and satisfy certain cancellation conditions. We show that the singular integral T f(x1, x2) = p. v.∫ Rn1+n2Ω(y′1, y′2)h(|y1|, |y2|)|y1|n1|y2|n2f(x1- y1, x2- y2)dy1dy2maps from Sα1, α2p, q˙F(Rn1× Rn2) boundedly to itself for 1 p, q ∞, α1, α2 ∈ R. 相似文献
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研究了退化弱(k1,k2)拟正则映射的正则性.利用H lder不等式、Sobolev空间的空间分析方法,以及内插定理等工具,给出了退化弱(k1,k2)拟正则映射事实上为退化(k1,k2)拟正则映射的一个充分条件,其结果对非退化情形也成立. 相似文献
9.
本文考虑空间 (k1,k2 ) -拟正则映射的 Lp(p >n)可积性 ,以及当 k1→ 1 ,k2 → 0时 p的渐近行为 . 相似文献
10.
设L是L2(Rn)上解析半群的无穷小生成算子,其积分核具有高斯界,L-α/2表示L的分数次积分算子,其中0<α<n.对自然数m,若bi(i=1,2,…,m)表示Rn上有界平均振荡函数,则由分数次积分L-α/2与bi(i=1,2,…,m)生成多线性交换子是从Lp(Rn)到Lq(Rn)是有界的,其中1<p<α/n,1/q=1/p-α/n. 相似文献
11.
Extreme points of the unit sphere S (L
1+L
∞ ) of LL
1+L
∞ under the classical norm used in the interpolation theory were characterized in [8] and [11], while extreme points of S(L
1 ∩ L
∞) under the classical norm were characterized in [7]. In this paper extreme points of the unit sphere of L
1+L
∞ and L
1 ∩ L
∞ under the “dual” norms are characterized. Moreover, all the extreme points in L
1 ∩ L
∞ and L
1+L
∞ (under both kinds of norms) are examined if they are exposed, H-points, or strongly exposed. Smooth points in both these
spaces for both the norms are also characterized. Finally, it is proved that in general the spaces L
p
+L
q
and L
p
∩ L
q
are not isometric to Orlicz spaces, provided that 1<p<q<+∞.
The paper was written while the first named author was visiting The University of Memphis
The third named author is supported by KBN-Grant 2 PO3A 050 09. 相似文献
12.
Abstract In this article, we prove a decomposition theorem for L2-convergent double sequences and introduce the notions of L2-Cauchy and L2*-Cauchy double sequence, and then study their certain properties. Finally, we introduce the notions of regularly (L2,L)- convergence and (L2, L)-Cauchy double sequence. 相似文献
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14.
J M Wilson 《The Journal of the Operational Research Society》2010,61(5):713-713
15.
Exact inequalities of Jackson-Stechkin type have been obtained for the average moduli of continuity of mth order (m ?? ?) with the weight function. The exact values of any n-widths were calculated for the function classes, which are defined by the majorant and the indicated average magnitudes. 相似文献
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A typical result of the paper isTheorem. LetE be a reflexive subspace ofL 1 (Ω, A, P) [(Ω,A, P) a probability space]. IfE contains a subspace isomorphic to lp then for every ε > 0,E contains a subspace (1 + ε) isomorphic to lp. The technics are probability theory and ultraproducts. 相似文献
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20.
Jay Rothman 《Journal of Fourier Analysis and Applications》1995,2(3):217-225
The Adler-Konheim theorem [Proc. Amer. Math. Soc. 13 (1962), 425-428] states that the collection of nth-order autocorrelation
functions
is a complete set of translation invariants for real-valued L1 functions on a locally compact abelian group. It is shown here that there are proper subsets of
that also form a complete set of translation invariants, and these subsets are characterized. Specifically, a subset is
complete if and only if it contains infinitely many even-order autocorrelation functions. In addition, any infinite subset
of
is complete up to a sign. While stated here for functions on
the proofs presented hold for functions on any locally compact abelian group that is not compact, in particular, on
and the integer lattice
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