共查询到20条相似文献,搜索用时 31 毫秒
1.
Let 1<q<∞, n(1−1/q)≤α<∞, 0<p<∞ and ω1,ω2 ɛA
1(R
n
) (the Muckenhoupt class). In this paper, the author introduce the weighted Herz-type Hardy spaces hk
q
α,p
(gw1,ω2) and present their atomic decomposition. Using the atomic decomposition, the author find out their dual spaces, establish
the boundedness on these spaces of the pseudo-differential operators of order zero and show thatD(R
n
), the class of C∞(Rn)-functions with compactly support, is dense inhK
q
α,p
(ω1,ω2) and there is a subsequence, which converges in distrbutional sense to some distribution ofhK
q
α,p
(ω1,ω2), of any bounded sequence inhK
q
α,p
(ω1,ω2). In addition, the author also set up the boundedness of some non-linear quantities in compensated compactness.
Supported by the NECF and the NECF and the NNSF of China. 相似文献
2.
3.
TieXin Guo 《中国科学A辑(英文版)》2008,51(9):1651-1663
Let (Ω,A,μ) be a probability space, K the scalar field R of real numbers or C of complex numbers,and (S,X) a random normed space over K with base (ω,A,μ). Denote the support of (S,X) by E, namely E is the essential supremum of the set {A ∈ A: there exists an element p in S such that X
p
(ω) > 0 for almost all ω in A}. In this paper, Banach-Alaoglu theorem in a random normed space is first established as follows: The random closed unit
ball S
*(1) = {f ∈ S
*: X
*
f
⩽ 1} of the random conjugate space (S
*,X
*) of (S,X) is compact under the random weak star topology on (S
*,X
*) iff E∩A=: {E∩A | A ∈ A} is essentially purely μ-atomic (namely, there exists a disjoint family {A
n
: n ∈ N} of at most countably many μ-atoms from E ∩ A such that E = ∪
n=1∞
A
n
and for each element F in E ∩ A, there is an H in the σ-algebra generated by {A
n
: n ∈ N} satisfying μ(FΔH) = 0), whose proof forces us to provide a key topological skill, and thus is much more involved than the corresponding
classical case. Further, Banach-Bourbaki-Kakutani-Šmulian (briefly, BBKS) theorem in a complete random normed module is established
as follows: If (S,X) is a complete random normed module, then the random closed unit ball S(1) = {p ∈ S: X
p
⩽ 1} of (S,X) is compact under the random weak topology on (S,X) iff both (S,X) is random reflexive and E ∩ A is essentially purely μ-atomic. Our recent work shows that the famous classical James theorem still holds for an arbitrary
complete random normed module, namely a complete random normed module is random reflexive iff the random norm of an arbitrary
almost surely bounded random linear functional on it is attainable on its random closed unit ball, but this paper shows that
the classical Banach-Alaoglu theorem and BBKS theorem do not hold universally for complete random normed modules unless they
possess extremely simple stratification structure, namely their supports are essentially purely μ-atomic. Combining the James
theorem and BBKS theorem in complete random normed modules leads directly to an interesting phenomenum: there exist many famous
classical propositions that are mutually equivalent in the case of Banach spaces, some of which remain to be mutually equivalent
in the context of arbitrary complete random normed modules, whereas the other of which are no longer equivalent to another
in the context of arbitrary complete random normed modules unless the random normed modules in question possess extremely
simple stratification structure. Such a phenomenum is, for the first time, discovered in the course of the development of
random metric theory. 相似文献
4.
Let f be an integrable function on the unit sphere Σ
n−1 of R
n
(n⩾3) and let σ
N
δ
be the Cesàro means of order σ of the Fourier-Laplace series of f. The special value λ:=n−2/2 of σ is known as the critical index. This paper proves that
and
where ω(f,t)p is the 1st-order modulus of continuity of f in Lp-metric which is defined in a way different than in the classical case of n=2.
In Memory of Professor M. T. Cheng
Project supported by the NSF of China under the grans # 19771009. 相似文献
5.
P. Danchev 《Lithuanian Mathematical Journal》2007,47(2):129-134
We prove the following theorem: Any abelian p-group is an n-Σ-group which is a strong ω-elongation of a totally projective group by a p
ω+n
-projective group precisely when it is totally projective. In particular, each p-torsion p
ω+n
-projective n-Σ-group is a direct sum of countable p-groups of length not exceeding ω + n and vice versa. These two claims generalize our recent results in [6] and [7].
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 2, pp. 155–162, April–June, 2007. 相似文献
6.
The distribution of the chromatic number on random graphsG
n, p
is quite sharply concentrated. For fixedp it concentrates almost surely in √n ω(n) consecutive integers where ω(n) approaches infinity arbitrarily slowly. If the average degreepn is less thann
1/6, it concentrates almost surely in five consecutive integers. Large deviation estimates for martingales are used in the proof. 相似文献
7.
A. V. Harutyunyan W. Lusky 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(3):128-135
Let U
n
be the unit polydisk in C
n
and S be the space of functions of regular variation. Let 1 ≤ p < ∞, ω = (ω
1, ..., ω
n
), ω
j
∈ S(1 ≤ j ≤ n) and f ∈ H(U
n
). The function f is said to be in holomorphic Besov space B
p
(ω) if
$
\left\| f \right\|_{B_p (\omega )}^p = \int_{U^n } {\left| {Df(z)} \right|^p \prod\limits_{j = 1}^n {\frac{{\omega _j (1 - |z_j |)}}
{{(1 - |z_j |^{2 - p} )}}} dm_{2n} (z) < + \infty }
$
\left\| f \right\|_{B_p (\omega )}^p = \int_{U^n } {\left| {Df(z)} \right|^p \prod\limits_{j = 1}^n {\frac{{\omega _j (1 - |z_j |)}}
{{(1 - |z_j |^{2 - p} )}}} dm_{2n} (z) < + \infty }
相似文献
8.
D. M. Israfilov 《Constructive Approximation》2001,17(3):335-351
Let G\subset C be a finite domain with a regular Jordan boundary L . In this work, the approximation properties of a p -Faber polynomial series of functions in the weighted Smirnov class E
p
(G,ω) are studied and the rate of polynomial approximation, for f∈ E
p
( G,ω) by the weighted integral modulus of continuity, is estimated. Some application of this result to the uniform convergence
of the Bieberbach polynomials π
n
in a closed domain \overline G with a smooth boundary L is given.
February 25, 1999. Date revised: October 20, 1999. Date accepted: May 26, 2000. 相似文献
9.
Given a permutation ω of {1, …, n}, let R(ω) be the root degree of ω, i.e. the smallest (prime) integer r such that there is a permutation σ with ω = σ
r
. We show that, for ω chosen uniformly at random, R(ω) = (lnlnn − 3lnlnln n + O
p
(1))−1 lnn, and find the limiting distribution of the remainder term.
Research supported in part by NSF grants CCR-0225610, DMS-0505550 and ARO grant W911NF-06-1-0076.
Research supported by NSF grant DMS-0406024. 相似文献
10.
S. A. Evdokimov M. A. Skopina 《Proceedings of the Steklov Institute of Mathematics》2009,265(1):143-147
It is shown that a “p-adic plane wave” f(t + ω
1
x
1 + ... + ω
n
x
n
), (t, x
1, ..., x
n
) ∈ ℚ
p
n + 1, where f is a Bruhat-Schwartz complex-valued test function and max1≤j≤n
|ω
j
|
p
= 1, satisfies, for any f, a certain homogeneous pseudodifferential equation, an analog of the classical wave equation. A theory of the Cauchy problem
for this equation is developed. 相似文献
11.
Qi Lü 《数学学报(英文版)》2010,26(12):2377-2386
In this paper, we establish a bang-bang principle of time optimal controls for a controlled parabolic equation of fractional order evolved in a bounded domain Ω of R^n, with a controller w to be any given nonempty open subset of Ω. The problem is reduced to a new controllability property for this equation, i.e. the null controllability of the system at any given time T 〉 0 when the control is restricted to be active in ω× E, where E is any given subset of [0, T] with positive (Legesgue) measure. The desired controllability result is established by means of a sharp observability estimate on the eigenfunctions of the Dirichlet Laplacian due to Lebeau and Robbiano, and a delicate result in the measure theory due to Lions. 相似文献
12.
E. V. Derets 《Ukrainian Mathematical Journal》2000,52(3):368-378
We establish lower bounds for the Kolmogorov widths d
2n-1(W
r
H
1ω.L
p
) and Gel’fand widths d
2n-1(W
r
H
1ω.L
p
) of the classes of functions W
r
H
1ω with a convex integral modulus of continuity ω(t). 相似文献
13.
Let G be a locally compact group, ω be a weight function on G and 1 < p < ∞. Here, we give a sufficient condition for that the weighted L
p
-space L
p
(G, ω) is a Banach algebra. Also, we get some necessary conditions on G and the weight function ω for L
p
(G, ω) to be a Banach algebra. As a consequence, we show that if G is abelian and L
p
(G, ω) is a Banach algebra, then G is σ-compact. 相似文献
14.
Shuichi Sato 《Arkiv f?r Matematik》1995,33(2):377-384
Weighted weak type estimates are proved for some maximal operators on the weighted Hardy spacesH
ω
p
(0 <p < 1, ω ∈A
1) (0<p<1, ω∞A1); in particular, weighted weak type endpoint estimates are obtained for the maximal operators arising from the Bochner-Riesz
means and the spherical means onH
ω
p
. 相似文献
15.
Vladimir Shpilrain 《Israel Journal of Mathematics》1995,91(1-3):307-316
LetE be a bounded Borel subset of ℝn,n≥2, of positive Lebesgue measure andP
E the corresponding ‘Pompeiu transform”. We prove thatP
E is injective onL
p(ℝn) if 1≤p≤2n/(n-1). We explore the connection between this problem and a Wiener-Tauberian type theorem for theM(n) action onL
q(ℝn) for various values ofq. We also take up the question of whenP
E is injective in caseE is of finite, positive measure, but is not necessarily a bounded set. Finally, we briefly look at these questions in the
contexts of symmetric spaces of compact and non-compact type. 相似文献
16.
We prove that a convex functionf ∈ L
p[−1, 1], 0<p<∞, can be approximated by convex polynomials with an error not exceeding Cω
3
ϕ
(f,1/n)p where ω
3
ϕ
(f,·) is the Ditzian-Totik modulus of smoothness of order three off. We are thus filling the gap between previously known estimates involving ω
3
ϕ
(f,1/n)p, and the impossibility of having such estimates involving ω4. We also give similar estimates for the approximation off by convexC
0 andC
1 piecewise quadratics as well as convexC
2 piecewise cubic polynomials.
Communicated by Dietrich Braess 相似文献
17.
Christopher S. Withers Saralees Nadarajah 《Methodology and Computing in Applied Probability》2011,13(4):855-871
Expressions are given for repeated upper tail integrals of the univariate normal density (and so also for the general Hermite
function) for both positive and negative arguments. The expressions involve moments of the form E(x + i N)
n
and E1 / (x
2 + N
2)
n
, where N is a unit normal random variable. Laplace transforms are provided for the Hermite functions and the moments. The practical
use of these expressions is illustrated. 相似文献
18.
Let Ω be a bounded co.nvex domain in Rn(n≥3) and G(x,y) be the Green function of the Laplace operator -△ on Ω. Let hrp(Ω) = {f ∈ D'(Ω) :(E)F∈hp(Rn), s.t. F|Ω = f}, by the atom characterization of Local Hardy spaces in a bounded Lipschitz domain, the bound of f→(△)2(Gf) for every f ∈ hrp(Ω) is obtained, where n/(n 1)<p≤1. 相似文献
19.
Veli B. SHAKHMUROV 《数学年刊B辑(英文版)》2008,29(1):95-112
This study focuses on the anisotropic Besov-Lions type spaces B^lp,θ(Ω;E0,E) associated with Banach spaces E0 and E. Under certain conditions, depending on l =(l1,l2,…,ln)and α=(α1,α2,…,αn),the most regular class of interpolation space Eα between E0 and E are found so that the mixed differential operators D^α are bounded and compact, from B^l+s p,θ(Ω;E0,E) to B^s p,θ(Ω;Eα).These results are applied to concrete vector-valued function spaces and to anisotropic differential-operator equations with parameters to obtain conditions that guarantee the uniform B separability with respect to these parameters. By these results the maximal B-regularity for parabolic Cauchy problem is obtained. These results are also applied to infinite systems of the quasi-elliptic partial differential equations and parabolic Cauchy problems with parameters to obtain sufficient conditions that ensure the same properties. 相似文献
20.
In this paper, we study the differentiable structure of the ω-subset of Sp(2n), which is formed by all matrices in Sp(2n) possessing ω as an eigenvalue, for ω on the unit circle in the complex plane. Based on this result the ω -index theory parametrized
by all ω on the unit circle for arbitrary symplectic paths is defined. 相似文献
|