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1.
Francisco L. Hernández Baltasar Rodriguez-Salinas 《Israel Journal of Mathematics》1998,104(1):191-220
We study the setP
X
of scalarsp such thatL
p
is lattice-isomorphically embedded into a given rearrangement invariant (r.i.) function spaceX[0, 1]. Given 0<α≤β<∞, we construct a family of Orlicz function spacesX=L
F
[0, 1], with Boyd indicesα andβ, whose associated setsP
X
are the closed intervals [γ, β], for everyγ withα≤γ≤β. In particular forα>2, this proves the existence of separable 2-convex r.i. function spaces on [0,1] containing isomorphically scales ofL
p
-spaces for different values ofp. We also show that, in general, the associated setP
X
is not closed. Similar questions in the setting of Banach spaces with uncountable symmetric basis are also considered. Thus,
we construct a family of Orlicz spaces ℓ
F
(I), with symmetric basis and indices fixed in advance, containing ℓ
p
(Γ-subspaces for differentp’s and uncountable Λ⊂I. In contrast with the behavior in the countable case (Lindenstrauss and Tzafriri [L-T1]), we show that the set of scalarsp for which ℓ
p
(Γ) is isomorphic to a subspace of a given Orlicz space ℓ
F
(I) is not in general closed.
Supported in part by DGICYT grant PB 94-0243. 相似文献
2.
Lattice-universal Orlicz function spacesL
F
α,β[0, 1] with prefixed Boyd indices are constructed. Namely, given 0<α<β<∞ arbitrary there exists Orlicz function spacesL
F
α,β[0, 1] with indices α and β such that every Orlicz function spaceL
G
[0, 1] with indices between α and β is lattice-isomorphic to a sublattice ofL
F
α,β[0, 1]. The existence of classes of universal Orlicz spacesl
Fα,β(I) with uncountable symmetric basis and prefixed indices α and β is also proved in the uncountable discrete case.
Partially supported by BFM2001-1284. 相似文献
3.
Let 1<α≦β<∞ andF be an arbitrary closed subset of the interval [α,β]. An Orlicz sequence spacel
φ (resp. an Orlicz function spaceL
φ(μ)) with associated indices α and β is found in such a way that the set of valuesp for which thel
p-space is isomorphic to a complemented subspace ofl
φ (resp.L
φ(μ)) is precisely the given setF (resp.F ∪ {2}). Also, a recent result of Hernández and Peirats [1] is extended showing that, even for the case in which the indices
satisfy αφ
∞<2<βφ
∞, there exist minimal Orlicz function spacesL
φ(μ) with no complemented copy ofl
p for anyp ≠ 2.
Supported in part by CAICYT grant 0338-84. 相似文献
4.
For anyp > 1, the existence is shown of Orlicz spacesL
F andl
F with indicesp containingsingular l
p-complemented copies, extending a result of N. Kalton ([6]). Also the following is proved:Let 1 <α ≦β < ∞and H be an arbitrary closed subset of the interval [α, β].There exist Orlicz sequence spaces l
F (resp. Orlicz function spaces LF)with indices α and β containing only singular l
p-complemented copies and such that the set of values p > 1for which l
p is complementably embedded into lF (resp. L
F)is exactly the set H (resp. H ∪ {2}). An explicitly defined class of minimal Orlicz spaces is given.
Supported in part by CAICYT grant 0338-84. 相似文献
5.
The Besov spacesB
p
α,μ
(Γ) and Triebel-Lizorkin spacesF
p
α,μ
(Γ) with high order α∈R on a Lipschitz curve Γ are defined. when 1≤p≤∞, 1≤q≤∞. To compare to the classical case a difference
characterization of such spaces in the case |α|<1 is given also.
The author is supported in part by the Foundation of Zhongshan University Advanced Research Centre and NSF of China. 相似文献
6.
An elementary proof of the (known) fact that each element of the Banach spaceℓ
w
p
(X) of weakly absolutelyp-summable sequences (if 1≤p<∞) in the Banach spaceX is the norm limit of its sections if and only if each element ofℓ
w
p
(X) is a norm null sequence inX, is given. Little modification to this proof leads to a similar result for a family of Orlicz sequence spaces. Some applications
to spaces of compact operators on Banach sequence spaces are considered. 相似文献
7.
On weighted approximation by Bernstein-Durrmeyer operators 总被引:6,自引:0,他引:6
Zhang Zhenqiu 《分析论及其应用》1991,7(2):51-64
In this paper, we consider weighted approximation by Bernstein-Durrmeyer operators in Lp[0, 1] (1≤p≤∞), where the weight function w(x)=xα(1−x)β,−1/p<α, β<1-1/p. We obtain the direct and converse theorems. As an important tool we use appropriate K-functionals.
Supported by Zhejiang Provincial Science Foundation. 相似文献
8.
D. Dacunha-Castelle 《Israel Journal of Mathematics》1972,13(3-4):261-276
The classL
p
the classes λ-SL
p
of spaces λ isomorphic to subspaces ofL
p
spaces and λ-QL
p
of subquotients have been characterized in the literature by formulas of certain simple forms. A theorem of Krivine gives
a general demonstration of these results in the framework of ψ normed spaces. In particular, characterizations of subspaces
and subquotients of certain classes of generalized Orlicz spaces are obtained.
相似文献
9.
Limin Sun 《Arkiv f?r Matematik》1995,33(1):173-182
Let Δ be the Laplace-Beltrami operator on ann dimensional completeC
∞ manifoldM In this paper we establish an estimate ofe
tΔ
(dμ) valid for allt>0 wheredμ is a locally uniformly α dimensional measure onM 0≤α≤n The result is used to study the mapping properties of (I-tΔ)-β considered as an operator fromL
p
(M dμ) toL
p
(M dx) wheredx is the Riemannian measure onM β>(n−α)/2p′ 1/p+1/p′=1 1≤p≤∞ 相似文献
10.
11.
This paper proves the existence of Orlicz function spaces Lφ (0, 1) containing no complemented subspaces isomorphic tol
p
for anyp ≠ 2. Some properties of minimal Orlicz function spaces Lφ (0, 1) are also given.
Supported in part by CAICYT grant 0338-84. 相似文献
12.
On the complemented subspaces problem 总被引:11,自引:0,他引:11
A Banach space is isomorphic to a Hilbert space provided every closed subspace is complemented. A conditionally σ-complete
Banach lattice is isomorphic to anL
p
-space (1≤p<∞) or toc
0(Γ) if every closed sublattice is complemented. 相似文献
13.
We investigate Besov spaces and their connection with trigonometric polynomial approximation inL
p[−π,π], algebraic polynomial approximation inL
p[−1,1], algebraic polynomial approximation inL
p(S), and entire function of exponential type approximation inL
p(R), and characterizeK-functionals for certain pairs of function spaces including (L
p[−π,π],B
s
a(L
p[−π,π])), (L
p(R),s
a(Lp(R))),
, and
, where 0<s≤∞, 0<p<1,S is a simple polytope and 0<α<r.
This project is supported by the National Science Foundation of China. 相似文献
14.
Min Guohua 《分析论及其应用》1992,8(3):28-37
In this paper, the Lp-convergence of Grünwald interpolation Gn(f,x) based on the zeros of Jacobi polynomials J
n
(α,β)
(x)(−1<α,β<1) is considered. Lp-convergence (0<p<2) of Grünwald interpolation Gn(f,x) is proved for p·Max(α,β)<1. Moreover, Lp-convergence (p>0) of Gn(f,x) is obtained for −1<α,β≤0. Therefore, the results of [1] and [3–5] are improved. 相似文献
15.
Ana Bela CRUZEIRO Xi Cheng ZHANG 《数学学报(英文版)》2006,22(1):101-104
For 1 〈 p ≤2, an L^p-gradient estimate for a symmetric Markov semigroup is derived in a general framework, i.e. ‖Γ^/2(Ttf)‖p≤Cp/√t‖p, where F is a carre du champ operator. As a simple application we prove that F1/2((I- L) ^-α) is a bounded operator from L^p to L^v provided that 1 〈 p 〈 2 and 1/2〈α〈1. For any 1 〈 p 〈 2, q 〉 2 and 1/2 〈α 〈 1, there exist two positive constants cq,α,Cp,α such that ‖Df‖p≤ Cp,α‖(I - L)^αf‖p,Cq,α(I-L)^(1-α)‖Df‖q+‖f‖q, where D is the Malliavin gradient ([2]) and L the Ornstein-Uhlenbeck operator. 相似文献
16.
J. Lindenstrauss proves in [L] thatc
0(Γ) is not quasicomplemented inl
∞(Γ) while H. P. Rosenthal in [R] proves that subspaces, whose dual balls are weak* sequentially compact and weak* separable,
are quasicomplemented inl
∞(Γ). In this note it is proved that weak* separability of the dual is the precise condition determining whether a subspace,
without isomorphic copies ofl
1 and whose dual balls are weak* sequentially compact, is quasicomplemented or not inl
∞(Γ). Especially spaces isomorphic tol
p(Γ), for 1<p<∞, have no quasicomplements inl
∞(Γ) if Γ is uncountable. 相似文献
17.
Yue XiukuiDept. of Math. Phys. Shandong Institute of Architecture Engineering Shandong China. 《高校应用数学学报(英文版)》2004,19(3):252-256
§1 IntroductionSuppose thatf is analytic in the open unit disc D in the complex plane.We defineMp(r,f) =12π∫2π0 | f(reiθ) | pdθ1 / p,0
相似文献
18.
A Banach space X will be called extensible if every operator E → X from a subspace E ⊂ X can be extended to an operator X → X. Denote by dens X. The smallest cardinal of a subset of X whose linear span is dense in X, the space X will be called automorphic when for every subspace E ⊂ X every into isomorphism T: E → X for which dens X/E = dens X/TE can be extended to an automorphism X → X. Lindenstrauss and Rosenthal proved that c
0 is automorphic and conjectured that c
0 and ℓ2 are the only separable automorphic spaces. Moreover, they ask about the extensible or automorphic character of c
0(Γ), for Γ uncountable. That c
0(Γ) is extensible was proved by Johnson and Zippin, and we prove here that it is automorphic and that, moreover, every automorphic
space is extensible while the converse fails. We then study the local structure of extensible spaces, showing in particular
that an infinite dimensional extensible space cannot contain uniformly complemented copies of ℓ
n
p
, 1 ≤ p < ∞, p ≠ 2. We derive that infinite dimensional spaces such as L
p
(μ), p ≠ 2, C(K) spaces not isomorphic to c
0 for K metric compact, subspaces of c
0 which are not isomorphic to c
0, the Gurarij space, Tsirelson spaces or the Argyros-Deliyanni HI space cannot be automorphic.
The work of the first author has been supported in part by project MTM2004-02635 相似文献
19.
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
20.
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