共查询到20条相似文献,搜索用时 46 毫秒
1.
Ferenc Weisz 《分析论及其应用》2000,16(1):52-65
The two-dimensional classical Hardy space Hp(T×T) on the bidisc are introduced, and it is shown that the maximal operator of the (C,α,β) means of a distribution is bounded
from the space Hp(T×T) to Lp(T2) (1/(α+1), 1/(β+1)<p≤∞), and is of weak type (H
1
#
(T×T), L1(T2)), where the Hardy space H
1
#
(T×T) is defined by the hybrid maximal function. As a consequence we obtain that the (C, α, β) means of a function f∈H
1
#
(T×T)⊃LlogL(T
2) convergs a. e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on the spaces
Hp(T×T) whenever 1/(α+1), 1(β+1)<p<∞. Thus, in case f∈Hp(T×T), the (C, α, β) means convergs to f in Hp(T×T) norm whenever (1/(α+1), 1/(β+1)<p<∞). The same results are proved for the conjugate (C, α, β) means, too.
This research was made while the author was visiting the Humboldt University in Berlin supported by the Alexander von Humboldt
Foundation. 相似文献
2.
Ferenc Weisz 《逼近论及其应用》2000,16(1):52-65
The two-dimensional classical Hardy space Hp(T×T) on the bidisc are introduced, and it is shown that the maximal operator of the (C,α,β) means of a distribution is bounded from the space Hp(T×T) to Lp(T2) (1/(α+1), 1/(β+1)<p≤∞), and is of weak type (H 1 # (T×T), L1(T2)), where the Hardy space H 1 # (T×T) is defined by the hybrid maximal function. As a consequence we obtain that the (C, α, β) means of a function f∈H 1 # (T×T)⊃LlogL(T 2) convergs a. e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on the spaces Hp(T×T) whenever 1/(α+1), 1(β+1)<p<∞. Thus, in case f∈Hp(T×T), the (C, α, β) means convergs to f in Hp(T×T) norm whenever (1/(α+1), 1/(β+1)<p<∞). The same results are proved for the conjugate (C, α, β) means, too. 相似文献
3.
V. A. Belonogov 《Algebra and Logic》2005,44(6):357-369
Let P(n) be the set of all partitions of a natural number n. In the representation theory of symmetric groups, for every partition
α ∈ P(n), the partition h(α) ∈ P(n) is defined so as to produce a certain set of zeros in the character table for Sn. Previously, the analog f(α) of h(α) was obtained pointing out an extra set of zeros in the table mentioned. Namely, h(α)
is greatest (under the lexicographic ordering ≤) of the partitions β of n such that χα(gβ) ≠ 0, and f(α) is greatest of the partitions γ of n that are opposite in sign to h(α) and are such that χα(gγ) ≠ 0, where χα is an irreducible character of Sn, indexed by α, and gβ is an element in the conjugacy class of Sn, indexed by β. For α ∈ P(n), under some natural restrictions, here, we construct new partitions h′(α) and f′(α) of n possessing
the following properties. (A) Let α ∈ P(n) and n ⩾ 3. Then h′(α) is identical is sign to h(α), χα(gh′(α)) ≠ 0, but χα(gγ) = 0 for all γ ∈ P(n) such that the sign of γ coincides with one of h(α), and h′(α) < γ < h(α). (B) Let α ∈ P(n), α ≠ α′,
and n ⩾ 4. Then f′(α) is identical in sign to f(α), χα(gf′(α)) ≠ 0, but χα(gγ) = 0 for all γ ∈ P(n) such that the sign of γ coincides with one of f(α), and f′(α) < γ < f(α). The results obtained are
then applied to study pairs of semiproportional irreducible characters in An.
Supported by RFBR grant No. 04-01-00463.
__________
Translated from Algebra i Logika, Vol. 44, No. 6, pp. 643–663, November–December, 2005. 相似文献
4.
Janusz Konieczny 《Central European Journal of Mathematics》2011,9(1):23-35
For an infinite set X, denote by Γ(X) the semigroup of all injective mappings from X to X under function composition. For α ∈ Γ(X), let C(α) = {β ∈ g/g(X): αβ = βα} be the centralizer of α in Γ(X). The aim of this paper is to determine those elements of Γ(X) whose centralizers have simple structure. We find α ∈ (X) such that various Green's relations in C(α) coincide, characterize α ∈ Γ(X) such that the $
\mathcal{J}
$
\mathcal{J}
-classes of C(α) form a chain, and describe Green's relations in C(α) for α with so-called finite ray-cycle decomposition. If α is a permutation, we also find the structure of C(α) in terms of direct and wreath products of familiar semigroups. 相似文献
5.
Ferenc Weisz 《Journal of Fourier Analysis and Applications》2000,6(4):389-401
The two-parameter dyadic martingale Hardy spacesH
p are introduced and it is proved that the maximal operator of the (C, α, β) means of a two-dimensional Walsh-Fourier series
is bounded from Hp to Lp (1/(α+1), 1/(β+1)<p<∞) and is of weak type (H
1
#
, L1), where the Hardy space H
1
#
is defined by the hybrid maximal function. As a consequence, we obtain that the (C, α, β) means of a function f∈H
1
#
converge a.e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on Hp whenever 1/(α+1), 1/(β+1)<p<∞. Thus in case f∈Hp, the (C, α, β) means converge to f in Hp norm. The same results are proved for the conjugate (C, α, β) means, too. 相似文献
6.
MiaoLI QuanZHENG 《数学学报(英文版)》2004,20(5):821-828
Let T = (T(t))t≥0 be a bounded C-regularized semigroup generated by A on a Banach space X and R(C) be dense in X. We show that if there is a dense subspace Y of X such that for every x ∈ Y, σu(A, Cx), the set of all points λ ∈ iR to which (λ - A)^-1 Cx can not be extended holomorphically, is at most countable and σr(A) N iR = Ф, then T is stable. A stability result for the case of R(C) being non-dense is also given. Our results generalize the work on the stability of strongly continuous senfigroups. 相似文献
7.
In this paper, which is a continuation of Timofte (J. Approx. Theory 119 (2002) 291–299, we give special uniform approximations of functions from CXY(T×S) and C∞(T×S,XY) by elements of the tensor products CX(T)CY(S), respectively C0(T,X)C0(S,Y), for topological spaces T,S and Γ-locally convex spaces X,Y (all four being Hausdorff). 相似文献
8.
Daniel W. Cunningham 《Archive for Mathematical Logic》2002,41(1):49-54
Jensen's celebrated Covering Lemma states that if 0# does not exist, then for any uncountable set of ordinals X, there is a Y∈L such that X⊆Y and |X| = |Y|. Working in ZF + AD alone, we establish the following analog: If ℝ# does not exist, then L(ℝ) and V have exactly the same sets of reals and for any set of ordinals X with |X| ≥Θ
L
(ℝ), there is a Y∈L(ℝ) such that X⊆Y and |X| = |Y|. Here ℝ is the set of reals and Θ is the supremum of the ordinals which are the surjective image of ℝ.
Received: 29 October 1999 / Published online: 12 December 2001 相似文献
9.
An Application of a Mountain Pass Theorem 总被引:3,自引:0,他引:3
We are concerned with the following Dirichlet problem:
−Δu(x) = f(x, u), x∈Ω, u∈H
1
0(Ω), (P)
where f(x, t) ∈C (×ℝ), f(x, t)/t is nondecreasing in t∈ℝ and tends to an L
∞-function q(x) uniformly in x∈Ω as t→ + ∞ (i.e., f(x, t) is asymptotically linear in t at infinity). In this case, an Ambrosetti-Rabinowitz-type condition, that is, for some θ > 2, M > 0,
0 > θF(x, s) ≤f(x, s)s, for all |s|≥M and x∈Ω, (AR)
is no longer true, where F(x, s) = ∫
s
0
f(x, t)dt. As is well known, (AR) is an important technical condition in applying Mountain Pass Theorem. In this paper, without assuming
(AR) we prove, by using a variant version of Mountain Pass Theorem, that problem (P) has a positive solution under suitable
conditions on f(x, t) and q(x). Our methods also work for the case where f(x, t) is superlinear in t at infinity, i.e., q(x) ≡ +∞.
Received June 24, 1998, Accepted January 14, 2000. 相似文献
10.
Denote by T(X) the semigroup of full transformations on a set X. For ε∈T(X), the centralizer of ε is a subsemigroup of T(X) defined by C(ε)={α∈T(X):αε=εα}. It is well known that C(id
X
)=T(X) is a regular semigroup. By a theorem proved by J.M. Howie in 1966, we know that if X is finite, then the subsemigroup generated by the idempotents of C(id
X
) contains all non-invertible transformations in C(id
X
). 相似文献
11.
Let Ω and Π be two finitely connected hyperbolic domains in the complex plane
\Bbb C{\Bbb C}
and let R(z, Ω) denote the hyperbolic radius of Ω at z and R(w, Π) the hyperbolic radius of Π at w. We consider functions f that are analytic in Ω and such that all values f(z) lie in the domain Π. This set of analytic functions is denoted by A(Ω, Π). We prove among other things that the quantities
Cn(W,P) := supf ? A(W,P)supz ? W\frac|f(n)(z)| R(f(z),P)n! (R(z,W))nC_n(\Omega,\Pi)\,:=\,\sup_{f\in A(\Omega,\Pi)}\sup_{z\in \Omega}\frac{\vert f^{(n)}(z)\vert\,R(f(z),\Pi)}{n!\,(R(z,\Omega))^n}
are finite for all
n ? \Bbb N{n \in {\Bbb N}}
if and only if ∂Ω and ∂Π do not contain isolated points. 相似文献
12.
Raffaele Mosca 《Graphs and Combinatorics》2001,17(3):517-528
Let G be a graph with n vertices, and denote as γ(G) (as θ(G)) the cardinality of a minimum edge cover (of a minimum clique cover) of G. Let E (let C) be the edge-vertex (the clique-vertex) incidence matrix of G; write then P(E)={x∈ℜ
n
:Ex≤1,x≥0}, P(C)={x∈ℜ
n
:Cx≤1,x≥0}, α
E
(G)=max{1
T
x subject to x∈P(E)}, and α
C
(G)= max{1
T
x subject to x∈P(C)}. In this paper we prove that if α
E
(G)=α
C
(G), then γ(G)=θ(G).
Received: May 20, 1998?Final version received: April 12, 1999 相似文献
13.
Let Ω be a domain with piecewise smooth boundary. In general, it is impossible to obtain a generalized solution u ∈ W
2
2
(Ω) of the equation Δ
x
2
u = f with the boundary conditions u = Δxu = 0 by solving iteratively a system of two Poisson equations under homogeneous Dirichlet conditions. Such a system is obtained
by setting v = −Δu. In the two-dimensional case, this fact is known as the Sapongyan paradox in the theory of simply supported
polygonal plates. In the present paper, the three-dimensional problem is investigated for a domain with a smooth edge Γ. If
the variable opening angle α ∈ C∞(Γ) is less than π everywhere on the edge, then the boundary-value problem for the biharmonic equation is equivalent to the
iterated Dirichlet problem, and its solution u inherits the positivity preserving property from these problems. In the case
α ∈ (π 2π), the procedure of solving the two Dirichlet problems must be modified by permitting infinite-dimensional kernel
and co-kernel of the operators and determining the solution u ∈ W
2
2
(Ω) by inverting a certain integral operator on the contour Γ. If α(s) ∈ (3π/2,2π) for a point s ∈ Γ, then there exists a
nonnegative function f ∈ L2(Ω) for which the solution u changes sign inside the domain Ω. In the case of crack (α = 2π everywhere on Γ), one needs to
introduce a special scale of weighted function spaces. In this case, the positivity preserving property fails. In some geometrical
situations, the problems on well-posedness for the boundary-value problem for the biharmonic equation and the positivity property
remain open. Bibliography: 46 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 336, 2006, pp. 153–198. 相似文献
14.
S. P. Yadav 《Acta Mathematica Hungarica》2003,98(1-2):21-30
Let X represent either the space C[-1,1] L
p
(α,β) (w), 1 ≦ p < ∞ on [-1, 1]. Then Xare Banach spaces under the sup or the p norms, respectively. We prove that there exists a normalized Banach subspace X
1
αβ of Xsuch that every f ∈ X
1
αβ can be represented by a linear combination of Jacobi polynomials to any degree of accuracy. Our method to prove such an approximation
problem is Fourier–Jacobi analysis based on the convergence of Fourier–Jacobi expansions.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
15.
Let A denote the class of functions which are analytic in |z|<1 and normalized so that f(0)=0 and f′(0)=1, and let R(α, β)⊂A
be the class of functions f such thatRe[f′(z)+αzf″(z)]>β,Re α>0, β<1. We determine conditions under which (i) f ∈ R(α1, β1), g ∈ R(α2, β2) implies that the convolution f×g of f and g is convex; (ii) f ∈ R(0, β1), g ∈ R(0, β2) implies that f×g is starlike; (iii) f≠A such that f′(z)[f(z)/z]μ-1 ≺ 1 + λz, μ>0, 0<λ<1, is starlike, and (iv) f≠A such that f′(z)+αzf″(z) ≺ 1 + λz, α>0, δ>0, is convex or starlike. Bibliography:
16 titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 138–154. 相似文献
16.
Arvid Perego 《Mathematische Zeitschrift》2009,262(3):571-583
The aim of this work is to give a generalization of Gabriel’s Theorem on coherent sheaves to coherent twisted sheaves on noetherian
schemes. We start by showing that we can recover a noetherian scheme X from the category Coh(X, α) of coherent α-twisted sheaves over X, where α lies in the cohomological Brauer group of X. This follows from the bijective correspondence between closed subsets of X and Serre subcategories of finite type of Coh(X, α). Moreover, any equivalence between Coh(X, α) and Coh(Y, β), where X and Y are noetherian schemes, and , β Br ′(Y) induces an isomorphism between X and Y. 相似文献
17.
Joanna Janczewska 《Central European Journal of Mathematics》2004,2(4):561-572
In this work we study the problem of the existence of bifurcation in the solution set of the equation F(x, λ)=0, where F: X×R
k
→Y is a C
2-smooth operator, X and Y are Banach spaces such that X⊂Y. Moreover, there is given a scalar product 〈·,·〉: Y×Y→R
1 that is continuous with respect to the norms in X and Y. We show that under some conditions there is bifurcation at a point (0, λ0)∈X×R
k
and we describe the solution set of the studied equation in a small neighbourhood of this point. 相似文献
18.
José M. Isidro 《Proceedings Mathematical Sciences》2009,119(5):635-645
Consider the space C0(Ω) endowed with a Banach lattice-norm ‖ · ‖ that is not assumed to be the usual spectral norm ‖ · ‖∞ of the supremum over Ω. A recent extension of the classical Banach-Stone theorem establishes that each surjective linear
isometry U of the Banach lattice (C
0(Ω), ‖ · ‖) induces a partition Π of Ω into a family of finite subsets S ⊂ Ω along with a bijection T: Π → Π which preserves cardinality, and a family [u(S): S ∈ Π] of surjective linear maps u(S): C(T(S)) → C(S) of the finite-dimensional C*-algebras C(S) such that
$
(Uf)|_{T(S)} = u(S)(f|_s ) \forall f \in \mathcal{C}_0 (\Omega ) \forall S \in \prod .
$
(Uf)|_{T(S)} = u(S)(f|_s ) \forall f \in \mathcal{C}_0 (\Omega ) \forall S \in \prod .
相似文献
19.
Let X be a normed space that satisfies the Johnson–Lindenstrauss lemma (J–L lemma, in short) in the sense that for any integer
n and any x
1,…,x
n
∈X, there exists a linear mapping L:X→F, where F⊆X is a linear subspace of dimension O(log n), such that ‖x
i
−x
j
‖≤‖L(x
i
)−L(x
j
)‖≤O(1)⋅‖x
i
−x
j
‖ for all i,j∈{1,…,n}. We show that this implies that X is almost Euclidean in the following sense: Every n-dimensional subspace of X embeds into Hilbert space with distortion
22O(log*n)2^{2^{O(\log^{*}n)}}
. On the other hand, we show that there exists a normed space Y which satisfies the J–L lemma, but for every n, there exists an n-dimensional subspace E
n
⊆Y whose Euclidean distortion is at least 2Ω(α(n)), where α is the inverse Ackermann function. 相似文献
20.
The aim of this paper is to obtain necessary and sufficient conditions for uniform exponential trichotomy of evolution families
on the real line. We prove that if p ∈ (1,∞) and the pair (Cb(R,X),Cc(R,X)) is uniformly p-admissible for an evolution family ={U(t,s)}t≥s then is uniformly exponentially trichotomic. After that we analyze when the uniform p-admissibility of the pair (Cb(R, X), Cc(R, X)) becomes a necessary condition for uniform exponential trichotomy. As applications of these results we study the uniform
exponential dichotomy of evolution families. We obtain that in certain conditions, the admissibility of the pair (Cb(R,X),Lp(R,X)) for an evolution family ={U(t,s)}t≥s is equivalent with its uniform exponential dichotomy. 相似文献
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