Packing constant for Cesàro-Orlicz sequence spaces

Zhen-Hua Ma; Li-Ning Jiang; Qiao-Ling Xin

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Displaying similar documents to “Packing constant for Cesàro-Orlicz sequence spaces”

Some results on packing in Orlicz sequence spaces

Y. Q. Yan (2001)

Studia Mathematica

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We present monotonicity theorems for index functions of N-fuctions, and obtain formulas for exact values of packing constants. In particular, we show that the Orlicz sequence space $l^{(N)}$ generated by the N-function N(v) = (1+|v|)ln(1+|v|) - |v| with Luxemburg norm has the Kottman constant $K (l^{(N)}) = N^{- 1} (1) / N^{- 1} (1 / 2)$ , which answers M. M. Rao and Z. D. Ren’s [8] problem.

An inequality in Orlicz function spaces with Orlicz norm

Jin Cai Wang (2003)

Commentationes Mathematicae Universitatis Carolinae

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We use Simonenko quantitative indices of an $𝒩$ -function $Φ$ to estimate two parameters $q_{Φ}$ and $Q_{Φ}$ in Orlicz function spaces $L^{Φ} [0, \infty)$ with Orlicz norm, and get the following inequality: $\frac{B_{Φ}}{B_{Φ} - 1} \leq q_{Φ} \leq Q_{Φ} \leq \frac{A_{Φ}}{A_{φ} - 1}$ , where $A_{Φ}$ and $B_{Φ}$ are Simonenko indices. A similar inequality is obtained in $L^{Φ} [0, 1]$ with Orlicz norm.

Decomposable sets and Musielak-Orlicz spaces of multifunctions

Andrzej Kasperski (2005)

Banach Center Publications

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We introduce the Musielak-Orlicz space of multifunctions $X_{m, φ}$ and the set $S_{F}^{φ}$ of φ-integrable selections of F. We show that some decomposable sets in Musielak-Orlicz space belong to $X_{m, φ}$ . We generalize Theorem 3.1 from [6]. Also, we get some theorems on the space $X_{m, φ}$ and the set $S_{F}^{φ}$ .

Fenchel-Orlicz spaces

Barry Turett

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CONTENTSIntroduction............................................................................... 51. Definitions and preliminary results......................................... 72. Completeness of $L^{Φ} (μ, ℜ)$ .............................. 93. Linear functionals on $L^{Φ} (μ, ℜ)$ ....................... 264. Geometry of Fenchel-Orlicz spaces........................................ 41References....................................................................................... 54

Nonlinear unilateral problems in Orlicz spaces

L. Aharouch, E. Azroul, M. Rhoudaf (2006)

Applicationes Mathematicae

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We prove the existence of solutions of the unilateral problem for equations of the type Au - divϕ(u) = μ in Orlicz spaces, where A is a Leray-Lions operator defined on $(A) \subset W ₀ ¹ L_{M} (Ω)$ , $μ \in L ¹ (Ω) + W^{- 1} E_{M ̅} (Ω)$ and $ϕ \in C ⁰ (ℝ, ℝ^{N})$ .

Some approximation results in Musielak-Orlicz spaces

Ahmed Youssfi, Youssef Ahmida (2020)

Czechoslovak Mathematical Journal

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We prove the continuity in norm of the translation operator in the Musielak-Orlicz $L_{M}$ spaces. An application to the convergence in norm of approximate identities is given, whereby we prove density results of the smooth functions in $L_{M}$ , in both the modular and norm topologies. These density results are then applied to obtain basic topological properties.

Dual spaces to Orlicz-Lorentz spaces

Anna Kamińska, Karol Leśnik, Yves Raynaud (2014)

Studia Mathematica

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For an Orlicz function φ and a decreasing weight w, two intrinsic exact descriptions are presented for the norm in the Köthe dual of the Orlicz-Lorentz function space $Λ_{φ, w}$ or the sequence space $λ_{φ, w}$ , equipped with either the Luxemburg or Amemiya norms. The first description is via the modular $i n f \int φ ⁎ (f * / | g |) | g | : g ≺ w$ , where f* is the decreasing rearrangement of f, ≺ denotes submajorization, and φ⁎ is the complementary function to φ. The second description is in terms of the modular $\int_{I} φ ⁎ ((f *) ⁰ / w) w$ ,where (f*)⁰ is Halperin’s level...

Some properties of packing measure with doubling gauge

Sheng-You Wen, Zhi-Ying Wen (2004)

Studia Mathematica

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Let g be a doubling gauge. We consider the packing measure $^{g}$ and the packing premeasure $₀^{g}$ in a metric space X. We first show that if $₀^{g} (X)$ is finite, then as a function of X, $₀^{g}$ has a kind of “outer regularity”. Then we prove that if X is complete separable, then $λ s u p ₀^{g} (F) \leq^{g} (B) \leq s u p ₀^{g} (F)$ for every Borel subset B of X, where the supremum is taken over all compact subsets of B having finite $₀^{g}$ -premeasure, and λ is a positive number depending only on the doubling gauge g. As an application, we show that for every doubling...

On some properties for dual spaces of Musielak-Orlicz function spaces

Zenon Zbąszyniak (2011)

Banach Center Publications

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We will present relationships between the modular ρ* and the norm in the dual spaces $(L_{Φ}) *$ in the case when a Musielak-Orlicz space $L_{Φ}$ is equipped with the Orlicz norm. Moreover, criteria for extreme points of the unit sphere of the dual space $(L ⁰_{Φ}) *$ will be presented.

Geometry of Orlicz spaces

Chen Shutao

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CONTENTSPreface..............................................................................................................................4Introduction........................................................................................................................51. Orlicz spaces..................................................................................................................6 1.1. Orlicz functions...........................................................................................................6 1.2....

Normal structure of Lorentz-Orlicz spaces

Pei-Kee Lin, Huiying Sun (1997)

Annales Polonici Mathematici

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Let ϕ: ℝ → ℝ₊ ∪ 0 be an even convex continuous function with ϕ(0) = 0 and ϕ(u) > 0 for all u > 0 and let w be a weight function. u₀ and v₀ are defined by u₀ = supu: ϕ is linear on (0,u), v₀=supv: w is constant on (0,v) (where sup∅ = 0). We prove the following theorem. Theorem. Suppose that $Λ_{ϕ, w} (0, \infty)$ (respectively, $Λ_{ϕ, w} (0, 1)$ ) is an order continuous Lorentz-Orlicz space. (1) $Λ_{ϕ, w}$ has normal structure if and only if u₀ = 0 (respectively, $\int^{v ₀} ϕ (u ₀) \cdot w < 2 a n d u ₀ < \infty) .$ (2) $Λ_{ϕ, w}$ has weakly normal structure if and only if $\int_{0}^{v ₀} ϕ (u ₀) \cdot w < 2$ .

A note on the open packing number in graphs

Mehdi Mohammadi, Mohammad Maghasedi (2019)

Mathematica Bohemica

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A subset $S$ of vertices in a graph $G$ is an open packing set if no pair of vertices of $S$ has a common neighbor in $G$ . An open packing set which is not a proper subset of any open packing set is called a maximal open packing set. The maximum cardinality of an open packing set is called the open packing number and is denoted by $ρ^{o} (G)$ . A subset $S$ in a graph $G$ with no isolated vertex is called a total dominating set if any vertex of $G$ is adjacent to some vertex of $S$ . The total domination number...

On certain porous sets in the Orlicz space of a locally compact group

Ibrahim Akbarbaglu, Saeid Maghsoudi (2012)

Colloquium Mathematicae

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Let G be a locally compact group with a fixed left Haar measure. Given Young functions φ and ψ, we consider the Orlicz spaces $L^{φ} (G)$ and $L^{ψ} (G)$ on a non-unimodular group G, and, among other things, we prove that under mild conditions on φ and ψ, the set $(f, g) \in L^{φ} (G) \times L^{ψ} (G) : f * g$ is well defined on G is σ-c-lower porous in $L^{φ} (G) \times L^{ψ} (G)$ . This answers a question raised by Głąb and Strobin in 2010 in a more general setting of Orlicz spaces. We also prove a similar result for non-compact locally compact groups.

The canonical injection of the Hardy-Orlicz space $H^{Ψ}$ into the Bergman-Orlicz space $^{Ψ}$

Pascal Lefèvre, Daniel Li, Hervé Queffélec, Luis Rodríguez-Piazza (2011)

Studia Mathematica

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We study the canonical injection from the Hardy-Orlicz space $H^{Ψ}$ into the Bergman-Orlicz space $^{Ψ}$ .

Lower bounds for Jung constants of Orlicz sequence spaces

Z. D. Ren (2010)

Annales Polonici Mathematici

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A new lower bound for the Jung constant $J C (l^{(Φ)})$ of the Orlicz sequence space $l^{(Φ)}$ defined by an N-function Φ is found. It is proved that if $l^{(Φ)}$ is reflexive and the function tΦ’(t)/Φ(t) is increasing on $(0, Φ^{- 1} (1)]$ , then $J C (l^{(Φ)}) \geq (Φ^{- 1} (1 / 2)) / (Φ^{- 1} (1))$ . Examples in Section 3 show that the above estimate is better than in Zhang’s paper (2003) in some cases and that the results given in Yan’s paper (2004) are not accurate.

An operator characterization of $L^{p}$ -spaces in a class of Orlicz spaces

Maciej Burnecki (2008)

Banach Center Publications

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We consider an embedding of the group of invertible transformations of [0,1] into the algebra of bounded linear operators on an Orlicz space. We show that if this embedding preserves the group action then the Orlicz space is an $L^{p}$ -space for some 1 ≤ p < ∞.

Packing four copies of a tree into a complete bipartite graph

Liqun Pu, Yuan Tang, Xiaoli Gao (2022)

Czechoslovak Mathematical Journal

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In considering packing three copies of a tree into a complete bipartite graph, H. Wang (2009) gives a conjecture: For each tree $T$ of order $n$ and each integer $k \geq 2$ , there is a $k$ -packing of $T$ in a complete bipartite graph $B_{n + k - 1}$ whose order is $n + k - 1$ . We prove the conjecture is true for $k = 4$ .

Reflexive subspaces of some Orlicz spaces

Emmanuelle Lavergne (2008)

Colloquium Mathematicae

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We show that when the conjugate of an Orlicz function ϕ satisfies the growth condition Δ⁰, then the reflexive subspaces of $L^{ϕ}$ are closed in the L¹-norm. For that purpose, we use (and give a new proof of) a result of J. Alexopoulos saying that weakly compact subsets of such $L^{ϕ}$ have equi-absolutely continuous norm.

The s-packing chromatic number of a graph

Wayne Goddard, Honghai Xu (2012)

Discussiones Mathematicae Graph Theory

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Let S = (a₁, a₂, ...) be an infinite nondecreasing sequence of positive integers. An S-packing k-coloring of a graph G is a mapping from V(G) to 1,2,...,k such that vertices with color i have pairwise distance greater than $a_{i}$ , and the S-packing chromatic number $χ_{S} (G)$ of G is the smallest integer k such that G has an S-packing k-coloring. This concept generalizes the concept of proper coloring (when S = (1,1,1,...)) and broadcast coloring (when S = (1,2,3,4,...)). In this paper, we consider...