共查询到20条相似文献,搜索用时 584 毫秒
1.
Let
be a unit sphere of the d–dimensional Euclidean space ℝ
d
and let
(0 < p ≤ 1) denote the real Hardy space on
For 0 < p ≤ 1 and
let
E
j
(f,H
p
) (j = 0, 1, ...) be the best approximation of f by spherical polynomials of degree less than or
equal to j, in the space
Given a distribution f on
its Cesàro mean of order δ > –1 is
denoted by
For 0 < p ≤ 1, it is known that
is the critical index for the uniform
summability of
in the metric H
p
. In this paper, the following result is proved:
Theorem
Let
0<p<1 and
Then for
where
A
N
(f)≈B
N
(f) means that there’s a positive constant C, independent of N and f, such that
In the case
d = 2, this result was proved by Belinskii in 1996.
The authors are partially supported by NNSF of China under the grant # 10071007 相似文献
2.
J. A. López Molina M. E. Puerta M. J. Rivera 《Bulletin of the Brazilian Mathematical Society》2006,37(2):191-216
Let
, be a family of compatible couples of Lp-spaces. We show that, given a countably incomplete ultrafilter
in
, the ultraproduct
of interpolation spaces defined by the real method is isomorphic to the direct sum of an interpolation space of type
, an intermediate K?the space between
and
being a purely atomic measure space, and a K?the function space K(Ω3) defined on some purely non atomic measure space (Ω3, ν3) in such a way that Ω2 ∪ Ω3 ≠∅.
The research of first and third authors is partially supported by the MEC and FEDER project MTM2004-02262 and AVCIT group
03/050. 相似文献
3.
Hidetoshi Maeda 《Archiv der Mathematik》2007,88(5):419-424
Let
be an ample vector bundle of rank n – 1 on a smooth complex projective variety X of dimension n≥ 3 such that X is a
-bundle over
and that
for any fiber F of the bundle projection
. The pairs
with
= 2 are classified, where
is the curve genus of
. This allows us to improve some previous results.
Received: 13 June 2006 相似文献
4.
Yah SUN Gen Xiang CHAI 《数学学报(英文版)》2007,23(4):685-696
In this article the following random intercept mixed effects model will be considered: yij = vi =v^τijβ+ εij,i=1,…,m;j=1,2,…,ni, where {vi} are i.i.d, random effects with mean α 2. 2 and finite variance σ^2 v, {εij} are i.i.d, random errors with finite variance ε^2 ε. Here we will estimate α,σ^2 v,σ^2 ε,β and study their large sample properties, such as strong consistency, strong convergence rates and asymptotic normality. 相似文献
5.
It is proved that the Stokes operator in Lq -space on an infinite cylindrical domain of
,
, with several exits to infinity generates a bounded and exponentially decaying analytic semigroup and admits a bounded
-calculus. For the resolvent estimates, the Stokes resolvent system with a prescribed divergence in an infinite straight
cylinder with bounded cross-section
is studied in L
q
where
and
is an arbitrary Muckenhoupt weight. The proofs use cut-off techniques and the theory of Schauder decomposition of UMD spaces based on
-boundedness of operator families and on square function estimates involving Muckenhoupt weights. 相似文献
6.
Abstract
With Littlewood–Paley analysis, Peetre and Triebel
classified, systematically, almost all the usual function spaces
into two classes of spaces: Besov spaces
and Triebel–Lizorkin
spaces
; but the structure of
dual spaces
of
is very different from
that of Besov spaces or that of Triebel–Lizorkin spaces, and
their structure cannot be analysed easily in the
Littlewood–Paley analysis. Our main goal is to characterize
in tent spaces with
wavelets. By the way, some applications are given: (i)
Triebel–Lizorkin spaces for p
= ∞ defined by Littlewood–Paley analysis cannot serve as the dual
spaces of Triebel–Lizorkin spaces for p = 1; (ii) Some inclusion relations
among these above spaces and some relations among
and
L
1
are studied.
Supported by NNSF of China (Grant No.
10001027) 相似文献
7.
Shan Zhen LU Li Fang XU 《数学学报(英文版)》2006,22(1):105-114
In this paper, the authors study the boundedness properties of μΩ↑m,b generated by the function b ∈Lipβ(R^n)(0 〈β≤ 1/m) and the Marcinkiewicz integrals operator μΩ. The boundednesses are established on the Hardy type spaces Hb^m^p,n(R^n) and the Herz Hardy type spaces Hbm Kq^α,p(R^b). 相似文献
8.
Adimurthi K. Sandeep 《NoDEA : Nonlinear Differential Equations and Applications》2007,13(5-6):585-603
Let Ω be a bounded domain in
, we prove the singular Moser-Trudinger embedding:
if and only if
where
and
. We will also study the corresponding critical exponent problem. 相似文献
9.
Let ∑ be either an oriented hyperplane or the unit sphere in
, let
be open and connected and let
be an open and connected domain in
such that
. If in
is a null solution of the Dirac operator (also called a monogenic function in
) which is continuously extendable to
, then conditions upon
are given enabling the monogenic extension of
across
. In such a way Schwarz reflection type principles for monogenic functions are established in the Spin (1) and Spin
cases. The Spin (1) case includes the classical Schwarz reflection principle for holomorphic functions in the plane. The
Spin
case deals with so-called “half boundary value problems” for the Dirac operator.
Received: 2 February 2006 相似文献
10.
We prove Tolokonnikov’s Lemma and the inner-outer factorization for the real Hardy space
, the space of bounded holomorphic (possibly operator-valued) functions on the unit disc all of whose matrix-entries (with
respect to fixed orthonormal bases) are functions having real Fourier coefficients, or equivalently, each matrix entry f satisfies
for all z ∈
.
Tolokonnikov’s Lemma for
means that if f is left-invertible, then f can be completed to an isomorphism; that is, there exists an F, invertible in
, such that F = [ f f
c
] for some f
c
in
. In control theory, Tolokonnikov’s Lemma implies that if a function has a right coprime factorization over
, then it has a doubly coprime factorization in
. We prove the lemma for the real disc algebra
as well. In particular,
and
are Hermite rings.
The work of the first author was supported by Magnus Ehrnrooth Foundation.
Received: December 5, 2006. Revised: February 4, 2007. 相似文献
11.
Ricardo Abreu Blaya Juan Bory Reyes Dixan Peña Peña Frank Sommen 《Advances in Applied Clifford Algebras》2007,17(2):145-152
Starting with an integral representation for the class of continuously differentiable solutions
of the system
where
is the complex Clifford algebra constructed over
are some suitable Clifford vectors and
their corresponding Dirac operators, we define the isotonic Cauchy transform and establish the Sokhotski-Plemelj formulae.
Some consequences of this result are also derived. 相似文献
12.
Stefan Gille 《Archiv der Mathematik》2007,88(4):333-343
Let
be a closed subscheme of the noetherian scheme X. We show that if X has a dualizing complex
then there exists a dualizing complex
of Z such that there is an isomorphism of coherent Witt groups
for all
.
Received: 3 March 2006 相似文献
13.
Here we study complete rotation hypersurfaces with constant k-th mean curvature Hk in
even and 2 < k < n. We prove the existence of a constant
such that there are no such hypersurfaces for
. We have only one compact hypersurface of this kind with
. For each
there is a corresponding family of complete immersed rotation hypersurfaces, each family containing two isoparametric hypersurfaces.
For Hk ≥ 0, there is also such a family, now containing only one isoparametric hypersurface. Finally, we prove the existence of
compact hypersurfaces with arbitrarily large Hk , neither isometric to a sphere nor to a product of spheres.
*Bull. Braz. Math. Soc. 30 (2), 1999, 139–161.
**Partially supported by FUNCAP, Brazil.
***Partially supported by CNPq, Brazil and DGAPA-UNAM, México. 相似文献
14.
Victor Katsnelson 《Complex Analysis and Operator Theory》2009,3(1):147-220
The paper deals with root location problems for two classes of univariate polynomials both of geometric origin. The first
class discussed, the class of Steiner polynomial, consists of polynomials, each associated with a compact convex set . A polynomial of this class describes the volume of the set V + tB
n
as a function of t, where t is a positive number and B
n
denotes the unit ball in . The second class, the class of Weyl polynomials, consists of polynomials, each associated with a Riemannian manifold , where is isometrically embedded with positive codimension in . A Weyl polynomial describes the volume of a tubular neighborhood of its associated as a function of the tube’s radius. These polynomials are calculated explicitly in a number of natural examples such as balls,
cubes, squeezed cylinders. Furthermore, we examine how the above mentioned polynomials are related to one another and how
they depend on the standard embedding of into for m > n. We find that in some cases the real part of any Steiner polynomial root will be negative. In certain other cases, a Steiner
polynomial will have only real negative roots. In all of this cases, it can be shown that all of a Weyl polynomial’s roots
are simple and, furthermore, that they lie on the imaginary axis. At the same time, in certain cases the above pattern does
not hold.
Erasmus Darwin, the nephew of the great scientist Charles Darwin, believed that sometimes one should perform the most unusual experiments. They usually yield no results but when they do . . . . So once he played trumpet in front of tulips for the whole day. The experiment yielded no results.Submitted: March 5, 2007., Revised: February 1, 2008., Accepted: February 2, 2008. 相似文献
15.
Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes 总被引:1,自引:0,他引:1
Yun Xia LI Li Xin ZHANG 《数学学报(英文版)》2006,22(1):143-156
In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai+kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞) is an absolutely solutely summable sequence of real numbers. 相似文献
16.
Let
be the L
2-critical nonlinear Schr?dinger equation, in a domain
with initial data in
(Dirichlet boundary condition) and
. We prove existence and stability of finite time blow-up dynamics with the log-log blow-up speed
Moreover, for a suitable class of finite time blow-up solutions, we derive global rigidity properties which turn out to be
modeled after the
ones.
Submitted: October 14, 2005. Revised: October 26, 2006. Accepted: February 2, 2007. 相似文献
17.
Some Limit Theorems for a Particle System of Single Point Catalytic Branching Random Walks 总被引:2,自引:0,他引:2
Vladimir VATUTIN Jie XIONG 《数学学报(英文版)》2007,23(6):997-1012
We study the scaling limit for a catalytic branching particle system whose particles perform random walks on Z and can branch at 0 only. Varying the initial (finite) number of particles, we get for this system different limiting distributions. To be more specific, suppose that initially there are n^β particles and consider the scaled process Zt^n(·) = Znt(√n·), where Zt is the measure-valued process 1 and to a representing the original particle system. We prove that Ztn converges to 0 when β 〈1/4 and to a nondegenerate discrete distribution when β=1/4.In addition,if 1/4〈β〈1/2 then n-^(2β-1/2)Zt^n converges to a random limit,while if β 〉21then n^-βZtn converges to a deterministic limit. 相似文献
18.
Let M be a compact hypersurface with constant scalar curvature one immersed into the unit Euclidean sphere
. As is well-known, such hypersurfaces can be characterized variationally as critical points of the integral
M
Hdv. In this paper we derive a sharp upper bound for the first eigenvalue of the corresponding Jacobi operator in terms of the mean curvature of the hypersurface. Moreover, we prove that this bound is achieved only for the Clifford tori in
with scalar curvature one.—Dedicated to the memory of Prof. José F. Escobar, Chepe 相似文献
19.
We show that the traveling salesman problem with triangle inequality cannot be approximated with a ratio better than
when the edge lengths are allowed to be asymmetric and
when the edge lengths are symmetric, unless P=NP. The best previous lower bounds were
and
respectively. The reduction is from H?stad’s maximum satisfiability of linear equations modulo 2, and is nonconstructive.
* Supported in part by NSF ITR Grant CCR-0121555.
† Supported by NSF award CCR-0307536 and a Sloan foundation fellowship. 相似文献
20.
A CDCSL algebra is a reflexive operator algebra with completely distributive and commutative subspace lattice. In this paper,
we show, for a weakly closed linear subspace
of a CDCSL algebra
, that
is a Lie ideal if and only if
for all invertibles A in
, and that
is a Jordan ideal if and only if it is an associative ideal. 相似文献