共查询到20条相似文献,搜索用时 15 毫秒
1.
Let ( Y,d,dl )\left( {\mathcal{Y},d,d\lambda } \right) be (ℝ
n
, |·|, μ), where |·| is the Euclidean distance, μ is a nonnegative Radon measure on ℝ
n
satisfying the polynomial growth condition, or the Gauss measure metric space (ℝ
n
, |·|, d
λ
), or the space (S, d, ρ), where S ≡ ℝ
n
⋉ ℝ+ is the (ax + b)-group, d is the left-invariant Riemannian metric and ρ is the right Haar measure on S with exponential growth. In this paper, the authors introduce and establish some properties of the atomic Hardy-type spaces
{ Xs ( Y ) }0 < s \leqslant ¥\left\{ {X_s \left( \mathcal{Y} \right)} \right\}_{0 < s \leqslant \infty } and the BMO-type spaces
{ BMO( Y, s ) }0 < s \leqslant ¥\left\{ {BMO\left( {\mathcal{Y}, s} \right)} \right\}_{0 < s \leqslant \infty }. Let H
1
( Y )\left( \mathcal{Y} \right) be the known atomic Hardy space and L
01
( Y )\left( \mathcal{Y} \right) the subspace of f ∈ L
1
( Y )\left( \mathcal{Y} \right) with integral 0. The authors prove that the dual space of X
s
( Y )\left( \mathcal{Y} \right) is BMO( Y,s )BMO\left( {\mathcal{Y},s} \right) when s ∈ (0,∞), X
s
( Y )\left( \mathcal{Y} \right) = H
1
( Y )\left( \mathcal{Y} \right) when s ∈ (0, 1], and X
∞
( Y )\left( \mathcal{Y} \right) = L
01
( Y )\left( \mathcal{Y} \right) (or L
1
( Y )\left( \mathcal{Y} \right)). As applications, the authors show that if T is a linear operator bounded from H
1
( Y )\left( \mathcal{Y} \right) to L
1
( Y )\left( \mathcal{Y} \right) and from L
1
( Y )\left( \mathcal{Y} \right) to L
1,∞
( Y )\left( \mathcal{Y} \right), then for all r ∈ (1,∞) and s ∈ (r,∞], T is bounded from X
r
( Y )\left( \mathcal{Y} \right) to the Lorentz space L
1,s
( Y )\left( \mathcal{Y} \right), which applies to the Calderón-Zygmund operator on (ℝ
n
, |·|, μ), the imaginary powers of the Ornstein-Uhlenbeck operator on (ℝ
n
, |·|, d
γ
) and the spectral operator associated with the spectral multiplier on (S, d, ρ). All these results generalize the corresponding results of Sweezy, Abu-Shammala and Torchinsky on Euclidean spaces. 相似文献
2.
Aubin Arroyo 《Bulletin of the Brazilian Mathematical Society》2007,38(3):455-465
In the context of Cr-flows on 3-manifolds (r ≥ 1), the notion of singular hyperbolicity, inspired on the Lorenz Attractor, is the right generalization of hyperbolicity
(in the sense of Smale) for C1-robustly transitive sets with singularities. We estabish conditions (on the associated linear Poincaré flow and on the nature
of the singular set) under which a transitive attractor with singularities of a C2-flow on a 3-manifold is singular hyperbolic. 相似文献
3.
This note deals with the orthogonality between sequences of random variables. The main idea of the note is to apply the results
on equidistant systems of points in a Hilbert space to the case of the space L
2(Ω, F, ℙ) of real square integrable random variables. The main result gives a necessary and sufficient condition for a particular
sequence of random variables (elements of which are taken from sets of equidistant elements of L
2(Ω, F, ℙ) to be orthogonal to some other sequence in L
2(Ω, F, ℙ). The result obtained is interesting from the point of view of the time series analysis, since it can be applied to a
class of sequences random variables that exhibit a monotonically increasing variance. An application to ergodic theorem is
also provided. 相似文献
4.
Heinrich P. Lotz 《Positivity》2008,12(1):119-132
We show that in the dual of Weak L1 the subspace of all rearrangement invariant continuous linear functionals is lattice isometric to a space L1(μ) and is the linear hull of the maximal elements of the dual unit ball. We also show that the dual of Weak L1 contains a norm closed weak* dense ideal which is lattice isometric to an ℓ1-sum of spaces of type C(K).
Helmut H. Schaefer in memoriam 相似文献
5.
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
6.
As the main result, we show that if G is a finite group such that Γ(G) = Γ(2
F
4(q)), where q = 22m+1 for some m ≧ 1, then G has a unique nonabelian composition factor isomorphic to 2
F
4(q). We also show that if G is a finite group satisfying |G| =|2
F
4(q)| and Γ(G) = Γ(2
F
4(q)), then G ≅ 2
F
4(q). As a consequence of our result we give a new proof for a conjecture of W. Shi and J. Bi for 2
F
4(q).
The third author was supported in part by a grant from IPM (No. 87200022). 相似文献
7.
8.
In this paper, the authors give the L
p
(1 < p < ∞ ) boundedness of the k-th order commutator of parabolic singular integral with the kernel function Ω ∈ L(log +
L)
k + 1(S
n − 1). The result in this paper is an extension of some known results.
The research was supported by NSF of China (Grant: 10571015) and SRFDP of China (Grant: 20050027025). 相似文献
9.
The following result is proved: Let be a n-dimensional C1-submanifold of RN which is domain of a given nRN-valued map of class C1. Then the set of all points P such that (P) is non-zero, simple and enveloped by TP is C2-rectifiable. As a corollary we get a criterion for the C2-rectifiability of a rectifiable set based on the rectifiability of some generalized Gauss lift to the Grassmanian bundle RN×G(N,n). Mathematics Subject Classification (2000) Primary 49Q15, 53A07; Secondary 49Q20, 49N60 相似文献
10.
Yun Qing Xu 《数学学报(英文版)》2009,25(8):1325-1336
A Latin squares of order v with ni missing sub-Latin squares (holes) of order hi (1 〈= i 〈 k), which are disjoint and spanning (i.e. ∑k i=l1 nihi = v), is called a partitioned incomplete Latin squares and denoted by PILS. The type of PILS is defined by (h1n1 h2n2…hknk ). If any two PILS inaset of t PILS of type T are orthogonal, then we denote the set by t-HMOLS(T). It has been proved that 3-HMOLS(2n31) exist for n ≥6 with 11 possible exceptions. In this paper, we investigate the existence of 3-HMOLS(2nu1) with u ≥ 4, and prove that 3-HMOLS(2~u1) exist if n ≥ 54 and n ≥7/4u + 7. 相似文献
11.
Area,coarea, and approximation in <Emphasis Type="Italic">W</Emphasis><Superscript>1,1</Superscript>
David Swanson 《Arkiv f?r Matematik》2007,45(2):381-399
Let Ω⊂ℝ
n
be an arbitrary open set. We characterize the space W
1,1
loc(Ω) using variants of the classical area and coarea formulas. We use these characterizations to obtain a norm approximation
and trace theorems for functions in the space W
1,1(ℝ
n
). 相似文献
12.
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
13.
U. Goginava 《Ukrainian Mathematical Journal》2005,57(11):1818-1824
In this paper, a necessary and sufficient condition for the inclusion of the class ΛBV in the class H
p
ω
is found.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 11, pp. 1557–1562, November, 2005. 相似文献
14.
Let A be an expanding n×n integer matrix with |det(A)|=m. Astandard digit set D for A is any complete set of coset representatives forℤ
n
/A(ℤ
n
). Associated to a given D is a setT (A, D), which is the attractor of an affine iterated function system, satisfyingT=∪
d∈D
(T+d). It is known thatT (A, D) tilesℝ
n
by some subset ofℤ
n
. This paper proves that every standard digit set D gives a setT (A, D) that tilesℝ
n
with a lattice tiling. 相似文献
15.
We prove that the G-invariant orbital measures supported on adjoint orbits in the Lie algebra of a classical, compact, connected, simple Lie
group satisfy a smoothness dichotomy: Either μ
k
is singular to Lebesgue measure or μ
k
∈ L
2. The minimum k for which μ
k
∈ L
2 is specified and is also the minimum k such that the k-fold sum of the orbit has positive measure.
S. K. Gupta appreciates the hospitality of the Department of Pure Mathematics at the University of Waterloo where some of
this research was done. K. E. Hare was supported in part by NSERC. 相似文献
16.
Jie Wang 《中国科学A辑(英文版)》2007,50(11):1642-1650
We obtain the Harnack estimate of the solution to Hk-flow in Euclidean space Rn 1,for k > 0.By using this estimate,we get some corollaries about the translation soliton. 相似文献
17.
P. Mironescu 《Journal of Mathematical Sciences》2010,170(3):340-355
We describe the structure of the space
Ws,p( \mathbbSn;\mathbbS1 ) {W^{s,p}}\left( {{\mathbb{S}^n};{\mathbb{S}^1}} \right) , where 0 < s < ∞ and 1 ≤ p < ∞. According to the values of s, p, and n, maps in
Ws,p( \mathbbSn;\mathbbS1 ) {W^{s,p}}\left( {{\mathbb{S}^n};{\mathbb{S}^1}} \right) can either be characterised by their phases or by a couple (singular set, phase). 相似文献
18.
Much of the recent literature on risk measures is concerned with essentially bounded risks in L
∞. In this paper we investigate in detail continuity and representation properties of convex risk measures on L
p
spaces. This frame for risks is natural from the point of view of applications since risks are typically modelled by unbounded
random variables. The various continuity properties of risk measures can be interpreted as robustness properties and are useful
tools for approximations. As particular examples of risk measures on L
p
we discuss the expected shortfall and the shortfall risk. In the final part of the paper we consider the optimal risk allocation
problem for L
p
risks. 相似文献
19.
LiangYuLIN ChunHuiQIU 《数学学报(英文版)》2004,20(6):989-998
Suppose that D is a bounded domain with a piecewise C^1 smooth boundary in C^n. Let ψ∈C^1 α(δD). By using the Hadamard principal value of the higher order singular integral and solid angle coefficient method of points on the boundary, we give the Plemelj formula of the higher order singular integral with the Boehner-Martinelli kernel, which has integral density ψ. Moreover, by means of the Plemelj formula and methods of complex partial differential equations, we discuss the corresponding Cauehy boundary value problem with the Boehner-Martinelli kernel on a closed piecewise smooth manifold and obtain its unique branch complex harmonic solution. 相似文献
20.
Gianluca Cassese 《应用数学学报(英文版)》2007,23(4):551-562
We prove an L~∞ version of the Yan theorem and deduce from it a necessary condition for theabsence of free lunches in a model of financial markets,in which asset prices are a continuous R~d valued processand only simple investment strategies are admissible.Our proof is based on a new separation theorem for convexsets of finitely additive measures. 相似文献