共查询到20条相似文献,搜索用时 31 毫秒
1.
A. Bonilla F. Pérez-González A. Stray R. Trujillo-González 《Journal d'Analyse Mathématique》1997,73(1):65-89
This paper is concerned with several approximation problems in the weighted Hardy spacesH
p(Ω) of analytic functions in the open unit disc D of the complex plane ℂ. We prove that ifX is a relatively closed subset of D, the class of uniform limits onX of functions inH
p(Ω) coincides, moduloH
p(Ω), with the space of uniformly continuous functions on a certain hull ofX which are holomorphic on its interior. We also solve the simultaneous approximation problems of describing Farrell and Mergelyan
sets forH
p(Ω), giving geometric characterizations for them. By replacing approximating polynomials by polynomial multipliers of outer
functions, our results lead to characterizations of the same sets with respect to cyclic vectors in the classical Hardy spacesH
p(D), 1 ⪯p < ∞.
Dedicated to Professor Nácere Hayek on the occasion of his 75th birthday. 相似文献
2.
Loukas GRAFAKOS 《中国科学A辑(英文版)》2008,51(12):2253-2284
Let X be an RD-space, i.e., a space of homogeneous type in the sense of Coifman and Weiss, which has the reverse doubling property. Assume that X has a dimension n. For α∈ (0, ∞) denote by Hαp(X ), Hdp(X ), and H?,p(X ) the corresponding Hardy spaces on X defined by the nontangential maximal function, the dyadic maximal function and the grand maximal function, respectively. Using a new inhomogeneous Calder′on reproducing formula, it is shown that all these Hardy spaces coincide with Lp(X ) when p ∈ (1, ∞] a... 相似文献
3.
In a recent paper, Ghenciu and Lewis studied strong Dunford-Pettis sets and made the following two assertions:
While the statements are correct, the proofs are flawed. The difficulty with the proofs is discussed, and a fundamental result
of Elton is used to establish a simple lemma which leads to quick proofs of both (1) and (2).
The online version of the original article can be found at . 相似文献
(1) | The Banach space X * contains a nonrelatively compact strong Dunford-Pettis set if and only if ℓ∞ ↪ X *. |
(2) | If c 0 ↪ Y and H is a complemented subspace of X so that H * is a strong Dunford-Pettis space, then W(X, Y) is not complemented in L(X, Y). |
4.
In a recent paper, Ghenciu and Lewis studied strong Dunford-Pettis sets and made the following two assertions:
While the statements are correct, the proofs are flawed. The difficulty with the proofs is discussed, and a fundamental result
of Elton is used to establish a simple lemma which leads to quick proofs of both (1) and (2). 相似文献
(1) | The Banach space X * contains a nonrelatively compact strong Dunford-Pettis set if and only if ℓ∞ ↪ X *. |
(2) | If c 0 ↪ Y and H is a complemented subspace of X so that H * is a strong Dunford-Pettis space, then W(X, Y) is not complemented in L(X, Y). |
5.
J. Wu 《Israel Journal of Mathematics》2010,178(1):349-391
Let X be a co-H-space of (p − 1)-cell complex with all cells in even dimensions. Then the loop space ΩX admits a retract Ā
min(X) that is the evaluation of the functor Ā
min on X. In this paper, we determine the homology H
*(Ā
min(X)) and give the EHP sequence for the spaces Ā
min(X). 相似文献
6.
Viorel Vâjâitu 《Czechoslovak Mathematical Journal》2010,60(3):655-667
Let X be a complex space of dimension n, not necessarily reduced, whose cohomology groups H
1(X, $
\mathcal{O}
$
\mathcal{O}
), ...,H
n−1(X, $
\mathcal{O}
$
\mathcal{O}
) are of finite dimension (as complex vector spaces). We show that X is Stein (resp., 1-convex) if, and only if, X is holomorphically
spreadable (resp., X is holomorphically spreadable at infinity). 相似文献
7.
Dominique Arlettaz 《Central European Journal of Mathematics》2004,2(1):50-56
This paper provides universal upper bounds for the exponent of the kernel and of the cokernel of the classical Boardman homomorphism
b
n
: π
n
(X)→H
n
(H;ℤ), from the cohomotopy groups to the ordinary integral cohomology groups of a spectrum X, and of its various generalizations π
n
(X)→E
n
(X), F
n
(X)→(E∧F)
n
(X), F
n
(X)→H
n
(X;π
0
F) and F
n
(X)→H
n+t
(X;π
t
F) for other cohomology theories E
*(−) and F
*(−). These upper bounds do not depend on X and are given in terms of the exponents of the stable homotopy groups of spheres and, for the last three homomorphisms, in
terms of the order of the Postnikov invariants of the spectrum F. 相似文献
8.
Shangquan BU 《数学年刊B辑(英文版)》2011,32(2):293-302
The author establishes operator-valued Fourier multiplier theorems on multi-dimensional Hardy spaces H
p
($
\mathbb{T}
$
\mathbb{T}
d
;X), where 1 ≤ p < ∞, d ∈ ℕ, and X is an AUMD Banach space having the property (α). The sufficient condition on the multiplier is a Marcinkiewicz type condition of order 2 using Rademacher boundedness of
sets of bounded linear operators. It is also shown that the assumption that X has the property (α) is necessary when d ≥ 2 even for scalar-valued multipliers. When the underlying Banach space does not have the property (α), a sufficient condition on the multiplier of Marcinkiewicz type of order 2 using a notion of d-Rademacher boundedness is also given. 相似文献
9.
R. A. McCoy 《Mathematica Slovaca》2010,60(4):541-570
We introduce a lower semicontinuous analog, L
−(X), of the well-studied space of upper semicontinuous set-valued maps with nonempty compact interval images. Because the elements
of L
−(X) contain continuous selections, the space C(X) of real-valued continuous functions on X can be used to establish properties of L
−(X), such as the two interrelated main theorems. The first of these theorems, the Extension Theorem, is proved in this Part
I. The Extension Theorem says that for binormal spaces X and Y, every bimonotone homeomorphism between C(X) and C(Y) can be extended to an ordered homeomorphism between L
−(X) and L
−(Y). The second main theorem, the Factorization Theorem, is proved in Part II. The Factorization Theorem says that for binormal
spaces X and Y, every ordered homeomorphism between L
−(X) and L
−(Y) can be characterized by a unique factorization. 相似文献
10.
Haïkel Skhiri 《Acta Appl Math》2010,112(3):347-356
Let m(T) and q(T) be respectively the minimum and the surjectivity moduli of T∈ℬ(X), where ℬ(X) denotes the algebra of all bounded linear operators on a complex Banach space X. If there exists a semi-invertible but non-invertible operator in ℬ(X) then, given a surjective unital linear map φ: ℬ(X)⟶ℬ(X), we prove that m(T)=m(φ(T)) for all T∈ℬ(X), if and only if, q(T)=q(φ(T)) for all T∈ℬ(X), if and only if, there exists a bijective isometry U∈ℬ(X) such that φ(T)=UTU
−1 for all T∈ℬ(X). 相似文献
11.
The multiplication map for global sections of line bundles and rank 1 torsion free sheaves on curves
E Ballico 《Proceedings Mathematical Sciences》2001,111(2):163-172
LetX be an integral projective curve andL ∃ Pica(X),M ∃ Picb (X) with h1(X, L)= h1(X, M) = 0 andL, M general. Here we study the rank of the multiplication map μ
L,M
:H
0(X,L)⊗H
0(X,M)→H
0(X,L⊗M). We also study the same problem whenL andM are rank 1 torsion free sheaves onX. Most of our results are forX with only nodes as singularities. 相似文献
12.
We investigate the completeness and completions of the normed algebras (D
(1)(X), ‖ · ‖) for perfect, compact plane sets X. In particular, we construct a radially self-absorbing, compact plane set X such that the normed algebra (D
(1)(X), ‖ · ‖) is not complete. This solves a question of Bland and Feinstein. We also prove that there are several classes of
connected, compact plane sets X for which the completeness of (D
(1)(X), ‖ · ‖) is equivalent to the pointwise regularity of X. For example, this is true for all rectifiably connected, polynomially convex, compact plane sets with empty interior, for
all star-shaped, compact plane sets, and for all Jordan arcs in ℂ. 相似文献
13.
We study the hyperspace K
0(X) of non-empty compact subsets of a Smyth-complete quasi-metric space (X, d). We show that K
0(X), equipped with the Hausdorff quasi-pseudometric H
d
forms a (sequentially) Yoneda-complete space. Moreover, if d is a T
1 quasi-metric, then the hyperspace is algebraic, and the set of all finite subsets forms a base for it. Finally, we prove
that K
0(X), H
d
) is Smyth-complete if (X, d) is Smyth-complete and all compact subsets of X are d
−1-precompact. 相似文献
14.
Vladimir Varlamov 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2010,138(6):1017-1031
Riesz fractional derivatives are defined as fractional powers of the Laplacian, D α = (?Δ) α/2 for ${\alpha \in \mathbb{R}}Riesz fractional derivatives are defined as fractional powers of the Laplacian, D
α
= (−Δ)
α/2 for
a ? \mathbbR{\alpha \in \mathbb{R}}. For the soliton solution of the Korteweg–de Vries equation, u
0(X) with X = x − 4t, these derivatives, u
α
(X) = D
α
u
0(X), and their Hilbert transforms, v
α
(X) = −HD
α
u
0(X), can be expressed in terms of the full range Hurwitz Zeta functions ζ+(s, a) and ζ−(s, a), respectively. New properties are established for u
α
(X) and v
α
(X). It is proved that the functions w
α
(X) = u
α
(X) + iv
α
(X) with α > −1 are solutions of the differential equation
-\fracddX(Pa(X)\fracdwdX)+Qa(X)w = lra(X)w, X ? \mathbbR,-\frac{\rm d}{{\rm d}X}\left(P_{\alpha}(X)\frac{{\rm d}w}{{\rm d}X}\right)+Q_{\alpha}(X)w = \lambda\rho_{\alpha}(X)w,\qquad X \in \mathbb{R}, 相似文献
15.
Let X be an infinite, locally connected, locally compact separable metrizable space. The space C(X) of real-valued continuous functions defined on X with the compact-open topology is a separable Fréchet space, so it is homeomorphic to the psuedo-interior s = (−1, 1)ℕ of the Hilbert cube Q = [−1, 1]ℕ. In this paper, generalizing the Sakai-Uehara’s result to the non-compact case, we construct a natural compactification $
\bar C
$
\bar C
(X) of C(X) such that the pair ($
\bar C
$
\bar C
(X), C(X)) is homeomorphic to (Q, s). In case X has no isolated points, this compactification $
\bar C
$
\bar C
(X) coincides with the space USCC
F
(X,
相似文献
16.
Let X={X(t),t∈ℝ
N
} be a Gaussian random field with values in ℝ
d
defined by
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