共查询到20条相似文献,搜索用时 31 毫秒
1.
Eiichi Nakai 《数学学报(英文版)》2008,24(8):1243-1268
Let X = (X, d,μ) The purpose of this paper is to be a space of homogeneous type in the sense of Coifman and Weiss. generalize the definition of Hardy space H^P(X) and prove that the generalized Hardy spaces have the same property as H^P(X). Our definition includes a kind of Hardy- Orlicz spaces and a kind of Hardy spaces with variable exponent. The results are new even for the R^n case. Let (X, δ, μ) be the normalized space of (X, d, μ) in the sense of Macias and Segovia. We also study the relations of our function spaces for (X, d, μ) and (X, δ,μ). 相似文献
2.
Hiroaki Aikawa Tero Kilpeläinen Nageswari Shanmugalingam Xiao Zhong 《Potential Analysis》2007,26(3):281-301
We establish a scale-invariant version of the boundary Harnack principle for p-harmonic functions in Euclidean C
1,1-domains and obtain estimates for the decay rates of positive p-harmonic functions vanishing on a segment of the boundary in terms of the distance to the boundary. We use these estimates
to study the behavior of conformal Martin kernel functions and positive p-superharmonic functions near the boundary of the domain.
H. A. was partially supported by Grant-in-Aid for (B) (2) (No. 15340046) Japan Society for the Promotion of Science. N. S.
was partially supported by NSF grant DMS-0355027. X. Z. was partially supported by the Taft foundation. 相似文献
3.
T. S. Kopaliani 《Ukrainian Mathematical Journal》2008,60(12):2006-2014
We point out that if the Hardy–Littlewood maximal operator is bounded on the space L
p(t)(ℝ), 1 < a ≤ p(t) ≤ b < ∞, t ∈ ℝ, then the well-known characterization of the spaces L
p
(ℝ), 1 < p < ∞, by the Littlewood–Paley theory extends to the space L
p(t)(ℝ). We show that, for n > 1 , the Littlewood–Paley operator is bounded on L
p(t) (ℝ
n
), 1 < a ≤ p(t) ≤ b < ∞, t ∈ ℝ
n
, if and only if p(t) = const.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1709–1715, December, 2008. 相似文献
4.
In this paper we characterize the Liouvillian integrable orthogonal separable Hamiltonian systems on T
2 for a given metric, and prove that the Hamiltonian flow on any compact level hypersurface has zero topological entropy. Furthermore,
by examples we show that the integrable Hamiltonian systems on T
2 can have complicated dynamical phenomena. For instance they can have several families of invariant tori, each family is bounded
by the homoclinic-loop-like cylinders and heteroclinic-loop-like cylinders. As we know, it is the first concrete example to
present the families of invariant tori at the same time appearing in such a complicated way.
This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 10671123, 10231020), “Dawn”
Program of Shanghai Education Comission of China (Grant No. 03SG10) and Program for New Century Excellent Tatents in University
of China (Grant No. 050391) 相似文献
5.
Humio Ichimura 《Mathematica Slovaca》2009,59(3):357-364
For an odd prime number p and an integer n ≥ 0, let h
n
be the class number of the p
n+1st cyclotomic field Q(). It is known that when p = 3 or 5, h
n
is odd for all n ≥ 0. We prove that the same holds also when p = 7.
The author was partially supported by Grant-in-Aid for Scientific Research (C), No. 19540005, Japan Society for the Promotion
of Science. 相似文献
6.
Let ƒ be a transcendental meromorphic function, a a nonzero finite complex number, and n ⩾ 2 a positive integer. Then ƒ + a(ƒ′)
n
assumes every complex value infinitely often. This answers a question of Ye for n = 2. A related normality criterion is also given.
This work was supported by the National Natural Science Foundation of China (Grant No. 10771076), the Natural Science Foundation
of Guangdong Province, China (Grant No. 07006700) and by the German-Israeli Foundation for Scientific Research and Development
(Grant No. G-809-234.6/2003) 相似文献
7.
We use microlocal and paradifferential techniques to obtain L
8 norm bounds for spectral clusters associated with elliptic second-order operators on two-dimensional manifolds with boundary.
The result leads to optimal L
q
bounds, in the range 2⩽q⩽∞, for L
2 - normalized spectral clusters on bounded domains in the plane and, more generally, for two-dimensional compact manifolds
with boundary. We also establish new sharp L
q
estimates in higher dimensions for a range of exponents q̅n⩽q⩽∞.
The authors were supported by the National Science Foundation, Grants DMS-0140499, DMS-0099642, and DMS-0354668. 相似文献
8.
We study property (T) and the fixed-point property for actions on L
p
and other Banach spaces. We show that property (T) holds when L
2 is replaced by L
p
(and even a subspace/quotient of L
p
), and that in fact it is independent of 1≤p<∞. We show that the fixed-point property for L
p
follows from property (T) when 1<p< 2+ε. For simple Lie groups and their lattices, we prove that the fixed-point property for L
p
holds for any 1< p<∞ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices
in products of general groups on superreflexive spaces.
Bader partially supported by ISF grant 100146; Furman partially supported by NSF grants DMS-0094245 and DMS-0604611; Gelander
partially supported by NSF grant DMS-0404557 and BSF grant 2004010; Monod partially supported by FNS (CH) and NSF (US). 相似文献
9.
R.?Antonio Gon?alves J.?A.?Martínez Alfaro? A.?Montesinos-Amilibia? M.?C.?Romero-Fuster? 《Bulletin of the Brazilian Mathematical Society》2007,38(2):157-178
We define the relative mean curvature directions on surfaces immersed in ℝn, n ≥ 4, generalizing the concept of mean curvature directions for surfaces in 4-space studied by Mello. We obtain their differential
equations and study their corresponding generic configurations.
*Work partially supported by DGCYT grant no. MTM2004-03244 and Unimontes-BR.
†Work partially supported by DGCYT grant no. MTM2004-03244.
‡Work partially supported by DGCYT grant no. BFM2003-0203. 相似文献
10.
Gaofei Zhang 《Israel Journal of Mathematics》2008,165(1):233-252
Let 0 < θ < 1 be an irrational number of bounded type. We proved that almost every point in the Julia set of e
2πiθ
sin (z) is an escaping point.
Partially supported by National Basic Research Program of China (973 Program) 2007CB814800. 相似文献
11.
Masakazu Yamagishi 《Archiv der Mathematik》2007,88(4):304-315
We introduce a condition analogous to the Nielsen-Schreier formula, and investigate basic properties of pro-p-groups satisfying the condition.
Partly supported by the Grant-in Aid for Scientific Research (C), Japan Society for the Promotion of Science.
Received: 23 January 2006 相似文献
12.
Michel Lavrauw Leo Storme Geertrui Van de Voorde 《Designs, Codes and Cryptography》2008,48(3):231-245
In this paper, we study the p-ary linear code C(PG(n,q)), q = p
h
, p prime, h ≥ 1, generated by the incidence matrix of points and hyperplanes of a Desarguesian projective space PG(n,q), and its dual code. We link the codewords of small weight of this code to blocking sets with respect to lines in PG(n,q) and we exclude all possible codewords arising from small linear blocking sets. We also look at the dual code of C(PG(n,q)) and we prove that finding the minimum weight of the dual code can be reduced to finding the minimum weight of the dual
code of points and lines in PG(2,q). We present an improved upper bound on this minimum weight and we show that we can drop the divisibility condition on the
weight of the codewords in Sachar’s lower bound (Geom Dedicata 8:407–415, 1979).
G. Van de Voorde’s research was supported by the Institute for the Promotion of Innovation through Science and Technology
in Flanders (IWT-Vlaanderen). 相似文献
13.
We study extension of operators T: E→ L0([0, 1]), where E is an F–function space and L0([0, 1]) the space of measurable functions with the topology of convergence in measure, to domains larger than E, and we study the properties of such domains. The main tool is the integration of scalar functions with respect to stochastic
measures and the corresponding spaces of integrable functions.
Partially supported by D.G.I. #MTM2006-13000-C03-01 (Spain). 相似文献
14.
Frame Wavelets with Compact Supports for L^2(R^n) 总被引:1,自引:0,他引:1
De Yun YANG King Wei ZHOU Zhu Zhi YUAN 《数学学报(英文版)》2007,23(2):349-356
The construction of frame wavelets with compact supports is a meaningful problem in wavelet analysis. In particular, it is a hard work to construct the frame wavelets with explicit analytic forms. For a given n × n real expansive matrix A, the frame-sets with respect to A are a family of sets in R^n. Based on the frame-sets, a class of high-dimensional frame wavelets with analytic forms are constructed, which can be non-bandlimited, or even compactly supported. As an application, the construction is illustrated by several examples, in which some new frame wavelets with compact supports are constructed. Moreover, since the main result of this paper is about general dilation matrices, in the examples we present a family of frame wavelets associated with some non-integer dilation matrices that is meaningful in computational geometry. 相似文献
15.
In this paper, we characterize, for 1≤p<∞, the multiple (p, 1)-summing multilinear operators on the product ofC(K) spaces in terms of their representing polymeasures. As consequences, we obtain a new characterization of (p, 1)-summing linear operators onC(K) in terms of their representing measures and a new multilinear characterization ofL
∞ spaces. We also solve a problem stated by M.S. Ramanujan and E. Schock, improve a result of H. P. Rosenthal and S. J. Szarek,
and give new results about polymeasures.
Both authors were partially supported by DGICYT grant BMF2001-1284. 相似文献
16.
Jia Gao 《高校应用数学学报(英文版)》2007,22(2):174-180
Let L^p(Ω, H^n) indicate the L^P-space of the maps for Heisenberg group target. In this paper some new properties are obtained for the space L^p(Ω, H^n) 相似文献
17.
Miklós CS 《中国科学A辑(英文版)》2007,50(10):1501-1520
General limit theorems are established for l
p
-valued Gaussian random fields indexed by a multidimensional parameter, which contain both almost sure moduli of continuity
and limits of large increments for the l
p
-valued Gaussian random fields under Ṅ explicit conditions.
This work was supported by NSERC Canada grants at Carleton University and by KOSEF-R01-2005-000-10696-0 相似文献
18.
Lawrence C. Evans Ovidiu Savin 《Calculus of Variations and Partial Differential Equations》2008,32(3):325-347
We propose a new method for showing C
1, α
regularity for solutions of the infinity Laplacian equation and provide full details of the proof in two dimensions. The
proof for dimensions n ≥ 3 depends upon some conjectured local gradient estimates for solutions of certain transformed PDE.
LCE is supported in part by NSF Grant DMS-0500452. OS was supported in part by the Miller Institute for Basic Research in
Science, Berkeley. 相似文献
19.
This paper considers some random processes of the form X
n+1=T
X
n
+B
n
(mod p) where B
n
and X
n
are random variables over (ℤ/pℤ)
d
and T is a fixed d×d integer matrix which is invertible over the complex numbers. For a particular distribution for B
n
, this paper improves results of Asci to show that if T has no complex eigenvalues of length 1, then for integers p relatively prime to det (T), order (log p)2 steps suffice to make X
n
close to uniformly distributed where X
0 is the zero vector. This paper also shows that if T has a complex eigenvalue which is a root of unity, then order p
b
steps are needed for X
n
to get close to uniformly distributed for some positive value b≤2 which may depend on T and X
0 is the zero vector. 相似文献
20.
Clear effects criterion is one of the important rules for selecting optimal fractional factorial designs, and it has become
an active research issue in recent years. Tang et al. derived upper and lower bounds on the maximum number of clear two-factor
interactions (2fi’s) in 2
n−(n−k) fractional factorial designs of resolutions III and IV by constructing a 2
n−(n−k) design for given k, which are only restricted for the symmetrical case. This paper proposes and studies the clear effects problem for the asymmetrical
case. It improves the construction method of Tang et al. for 2
n−(n−k) designs with resolution III and derives the upper and lower bounds on the maximum number of clear two-factor interaction
components (2fic’s) in 4
m
2
n
designs with resolutions III and IV. The lower bounds are achieved by constructing specific designs. Comparisons show that
the number of clear 2fic’s in the resulting design attains its maximum number in many cases, which reveals that the construction
methods are satisfactory when they are used to construct 4
m
2
n
designs under the clear effects criterion.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 10571093, 10671099 and 10771123),
the Research Foundation for Doctor Programme (Grant No. 20050055038) and the Natural Science Foundation of Shandong Province
of China (Grant No. Q2007A05). Zhang’s research was also supported by the Visiting Scholar Program at Chern Institute of Mathematics. 相似文献