共查询到20条相似文献,搜索用时 15 毫秒
1.
In this note we give a simple proof that every subspace of Lp, 2 < p < ∞, with an unconditional basis has an equivalent norm determined by partitions and weights. Consequently Lp has a norm determined by partitions and weights.
Received: 31 January 2005 相似文献
2.
We show norm estimates for the sum of independent random variables in noncommutative L
p
-spaces for 1 < p < ∞, following our previous work. These estimates generalize the classical Rosenthal inequality in the commutative case.
As applications, we derive an equivalence for the p-norm of the singular values of a random matrix with independent entries, and characterize those symmetric subspaces and unitary
ideals which can be realized as subspaces of a noncommutative L
p
for 2 < p < ∞.
The first author is partially supported by the National Science Foundation DMS-0301116.
The second author is partially supported by the Agence Nationale de Recherche 06-BLAN-0015. 相似文献
3.
Song LI Guo Mao WANG Zhi Song LIU 《数学学报(英文版)》2005,21(6):1475-1486
The purpose of this paper is to investigate the mean size formula of wavelet packets in Lp for 0 〈 p ≤ ∞. We generalize a mean size formula of wavelet packets given in terms of the p-norm joint spectral radius and we also give some asymptotic formulas for the Lp-norm or quasi-norm on the subdivision trees. All results will be given in the general setting, 相似文献
4.
Daniel Pellegrino Eduardo V. Teixeira 《Bulletin of the Brazilian Mathematical Society》2009,40(3):417-431
The main result of the paper shows that, for 1 < p < ∞ and 1 ≤ q < ∞, a linear operator T: ℓ
p
→ ℓ
q
attains its norm if, and only if, there exists a not weakly null maximizing sequence for T (counterexamples can be easily constructed when p = 1). For 1 < p ≠ q < ∞, as a consequence of the previous result we show that any not weakly null maximizing sequence for a norm attaining operator
T: ℓ
p
→ ℓ
q
has a norm-convergent subsequence (and this result is sharp in the sense that it is not valid if p = q). We also investigate lineability of the sets of norm-attaining and non-norm attaining operators. 相似文献
5.
Extreme points of the unit sphere S (L
1+L
∞ ) of LL
1+L
∞ under the classical norm used in the interpolation theory were characterized in [8] and [11], while extreme points of S(L
1 ∩ L
∞) under the classical norm were characterized in [7]. In this paper extreme points of the unit sphere of L
1+L
∞ and L
1 ∩ L
∞ under the “dual” norms are characterized. Moreover, all the extreme points in L
1 ∩ L
∞ and L
1+L
∞ (under both kinds of norms) are examined if they are exposed, H-points, or strongly exposed. Smooth points in both these
spaces for both the norms are also characterized. Finally, it is proved that in general the spaces L
p
+L
q
and L
p
∩ L
q
are not isometric to Orlicz spaces, provided that 1<p<q<+∞.
The paper was written while the first named author was visiting The University of Memphis
The third named author is supported by KBN-Grant 2 PO3A 050 09. 相似文献
6.
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
7.
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
8.
In the paper, we characterize the coefficient multiplier spaces of mixed norm spaces (H
p,q
(φ1), H
u,v
(φ2)) for the values of p, q, u, v in three cases: (i) 0 < p ≤ u ≤ ∞, 0 < q ≤ min(1, v) ≤ ∞. (ii) v = ∞, 0 < p ≤ u ≤ ∞, 1 ≤ u, q ≤ ∞. (iii) 1 ≤ v ≤ 2 ≤ q ≤ ∞, and 0 < p ≤ u ≤ ∞ or 1 ≤ p, u ≤ ∞. The first case extends the result of Blasco, Jevtić, and Pavlović in one variable. The third case generalizes partly
the results of Jevtić, Jovanović, and Wojtaszczyk to higher dimensions.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
9.
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
10.
V. A. Martirosyan S. E. Mkrtchyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(3):162-169
The paper presents some new results on approximation by polynomials with gaps in the norm of the space L
p
, 1 ≤ p < ∞, on non-Caratheodory domains in the complex plane. Lacunary versions of several results due to A. L. Shahinian, M. M.
Djrbashian, S. M. Mergelian and J. Brennan are proved. 相似文献
11.
In this paper, we continue studying the so-called non-linear best m-term one-sided approximation problems and obtain the asymptotic estimations of non-linear best m-term one-sided trigonometric approximation under the norm Lp (1 ≤ p ≤ ∞) of multiplier function classes and the corresponding m-term Greedy-liked one-sided trigonometric approximation results. 相似文献
12.
We define the notion of “stable Banach space” by a simple condition on the norm. We prove that ifE is a stable Banach space, then every subspace ofL
p(E) (1≦p<∞) is stable. Our main result asserts that every infinite dimensional stable Banach space containsl
p, for somep, 1≦p<∞. This is a generalization of a theorem due to D. Aldous: every infinite dimensional subspace ofL
1 containsl
p, for somep in the interval [1, 2]. 相似文献
13.
Marshall Ash 《Journal of Fourier Analysis and Applications》2010,16(6):1053-1069
Let P be a polygon in ℤ2 and consider the mapping of an
L1(\mathbbT2)L^{1}(\mathbb{T}^{2})
function into the partial sum of its Fourier series determined by the dilate of P by the integer N. If the image space is endowed with the L
p
norm, 1<p<∞, then the operator norm will be given by the L
p
norm of ∑(m,n)∈NP
e
2π
i(mx+ny). The size of this operator norm is shown to be O(N
2(1−1/p)) when the polygon is a triangle. The estimate is independent of the shape of the triangle. For a k sided polygon the corresponding estimate is O(kN
2(1−1/p)). 相似文献
14.
Quanhua Xu 《Israel Journal of Mathematics》1995,91(1-3):173-187
Let (Ω,F, P) be a probability space and {F
n}n≥0 a regular increasing sequence of sub-σ-fields ofF. LetH
1(Ω) be the usual Hardy space ofF
n-martingales. We show that the couple (H
1(Ω),L
∞(Ω)) is a partial retract of (L
1(Ω),L
∞(Ω)). It is also proved that (L
p(Ω),BMO(Ω)) is a partial retract of (L
p(Ω),L
∞(Ω)) for all 1<p<∞. 相似文献
15.
It is proved that for every 1≦p<∞, 1≦q<∞ and for every sequence {p
n}, 1≦p
n<∞,p
n→p, the spaceX=(Σ⊕l
p
n)
q
(resp.U=(Σ⊕L
p
n(0, 1))
q
) is uniformly homeomorphic toX⊕l
p (resp.U⊕L
p(0, 1)). This extends Ribe’s result from the casep=1 to generalp<∞ and thus provides examples of uniformly convex, uniformly homeomorphic Banach spaces which are not Lipschitz equivalent. 相似文献
16.
Fang Gensun 《中国科学A辑(英文版)》2001,44(9):1126-1131
The main result of this paper asserts that if a function f is in the class Bπ,p, 1 <p < ∞; that is, those p-integrable functions whose Fourier transforms are supported in the interval [ - π, π], then f and its
derivatives f(j) j = 1, 2, …, can be recovered from its sampling sequence{f(k)} via the cardinal interpolating spline of degree m in the metric
ofL
q(ℝ)), 1 <p=q < ∞, or 11 <p=q < ⩽ ∞. 相似文献
17.
Alexander Gorodnik 《Israel Journal of Mathematics》2004,140(1):125-144
In this paper we establish dimension freeL
p
(ℝ
n
,|x|α) norm inequalities (1<p<∞) for the oscillation and variation of the Riesz transforms in ℝ
n
. In doing so we findA
p
-weighted norm inequalities for the oscillation and the variation of the Hilbert transform in ℝ. Some weighted transference
results are also proved.
Partially supported by European Commission via the TMR network “Harmonic Analysis”. 相似文献
18.
《Arkiv f?r Matematik》1992,30(1):217-220
We determine the smallest Schatten class containing all integral operators with kernels inL
p(Lp', q)symm, where 2 <p∞ and 1≦q≦∞. In particular, we give a negative answer to a problem posed by Arazy, Fisher, Janson and Peetre in [1].
Supported in part by DGICYT (SAB-90-0033). 相似文献
19.
Denote by B
2σ,p
(1 < p < ∞) the bandlimited class p-integrable functions whose Fourier transform is supported in the interval [−σ, σ]. It is shown that a function in B
2σ,p
can be reconstructed in L
p(ℝ) by its sampling sequences {f (κπ / σ)}
κ∈ℤ and {f’ (κπ / σ)}
κ∈ℤ using the Hermite cardinal interpolation. Moreover, it will be shown that if f belongs to L
p
r
(ℝ), 1 < p < ∞, then the exact order of its aliasing error can be determined.
Project supported by the Scientific Research Common Program of Beijing Municipal Commission of Education under grant number
KM 200410009010 and by the Natural Science Foundation of China under grant number 10071006 相似文献
20.
Jean-Marie Mirebeau 《Numerische Mathematik》2012,120(2):271-305
Given a function f defined on a bounded polygonal domain
W ì \mathbbR2{\Omega \subset \mathbb{R}^2} and a number N > 0, we study the properties of the triangulation TN{\mathcal{T}_N} that minimizes the distance between f and its interpolation on the associated finite element space, over all triangulations of at most N elements. The error is studied in the W
1, p
semi-norm for 1 ≤ p < ∞, and we consider Lagrange finite elements of arbitrary polynomial order m − 1. We establish sharp asymptotic error estimates as N → +∞ when the optimal anisotropic triangulation is used. A similar problem has been studied in Babenko et al. (East J Approx.
12(1):71–101, 2006), Cao (J Numer Anal. 45(6):2368–2391, 2007), Chen et al. (Math Comput. 76:179–204, 2007), Cohen (Multiscale, Nonlinear and Adaptive Approximation. Springer, Berlin, 2009), Mirebeau (Constr Approx. 32(2):339–383, 2010), but with the error measured in the L
p
norm. The extension of this analysis to the W
1, p
norm is required in order to match more closely the needs of numerical PDE analysis, and it is not straightforward. In particular,
the meshes which satisfy the optimal error estimate are characterized by a metric describing the local aspect ratio of each
triangle and by a geometric constraint on their maximal angle, a second feature that does not appear for the L
p
error norm. Our analysis also provides with practical strategies for designing meshes such that the interpolation error satisfies
the optimal estimate up to a fixed multiplicative constant. 相似文献