共查询到20条相似文献,搜索用时 0 毫秒
1.
Prediction in Orlicz spaces 总被引:1,自引:0,他引:1
In this paper, we investigate the prediction (or best approximation) operator from a uniformly convex real Orlicz space to a subset of -lattice measurable functions. In particular, a counterexample to the monotoncity property, which holds in Lp spaces, is given. Also, a sufficient condition for monotonicity to hold is given. Finally, nested -lattices, as occur in isotonic regression, are considered.This author supported by a grant from the Indiana University-Purdue University at Fort Wayne Research and Instructional Development Support Program 相似文献
2.
3.
Andrea Cianchi 《Transactions of the American Mathematical Society》1999,351(6):2459-2478
We establish a sharp extension, in the framework of Orlicz spaces, of the (-dimensional) Hardy inequality, involving functions defined on a domain , their gradients and the distance function from the boundary of .
4.
5.
It is shown that an Orlicz sequence space admits an equivalent analytic renorming if and only if it is either isomorphic to or isomorphically polyhedral. As a consequence, we show that there exists a separable Banach space admitting an equivalent -Fréchet norm, but no equivalent analytic norm.
6.
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
7.
A. E. Mikhailov 《Journal of Mathematical Sciences》1988,43(6):2826-2829
We give sufficient conditions for random elements of L1(T, , ) to belong to L(T, Ol,) the Orlicz space.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 127–132, 1987. 相似文献
8.
We prove some direct and converse theorems of trigonometric approximation in weighted Orlicz spaces with weights satisfying
so called Muckenhoupt’s A
p
condition. 相似文献
9.
E. Lami Dozo 《Milan Journal of Mathematics》1985,55(1):175-179
10.
11.
12.
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
13.
14.
An inverse theorem of the trigonometric approximation theory in Weighted Orlicz spaces is proved and the constructive characterization of the generalized Lipschitz classes defined in these spaces is obtained. 相似文献
15.
16.
Henryk Hudzik 《Indagationes Mathematicae》2007,18(2):215-231
Given a weight w in Ω ⊂ ∝N, |Ω| < ∞ and a Young function φ, we consider the weighted modular ∫Ω ω(f(x))w(x)dx and the resulting weighted Orlicz space Lω(w). For a Young function Ω ∉ Δ2(∞) we present a necessary and sufficient conditions in order that Lω(w) = Lω(XΩ) up to the equivalence of norms. We find a necessary and sufficient condition for ω in order that there exists an unbounded weight w such that the above equality of spaces holds. By way of applications we simplify criteria from [5] for continuity of the composition operator from Lω into itself when ω Δ2(∞) and obtain necessary and sufficient condition in order that the composition operator maps Lω. continuously onto Lω. 相似文献
17.
The Lipschitz classes Lip(α, M) , 0 α≤ 1 are defined for Orlicz space generated by the Young function M, and the degree of approximation by matrix transforms of f ∈ Lip (α, M) is estimated by n-α . 相似文献
18.
Hiro-o Kita 《Proceedings of the American Mathematical Society》1996,124(10):3019-3025
Let and be the functions having the representations and , where is a positive continuous function such that and is quasi-increasing. Then the maximal function is a function in Orlicz space for all if and only if there exists a positive constant such that for all .
19.
We exhibit balance conditions between a Young function A and a Young function B for a Korn type inequality to hold between the LB norm of the gradient of vector-valued functions and the LA norm of its symmetric part. In particular, we extend a standard form of the Korn inequality in Lp, with 1<p<∞, and an Orlicz version involving a Young function A satisfying both the Δ2 and the ∇2 condition. 相似文献
20.