Nonsquareness and Locally Uniform Nonsquareness in Orlicz-Bochner Function Spaces Endowed with Luxemburg Norm [PDF]
Journal of Inequalities and Applications, 2011 Criteria for nonsquareness and locally uniform nonsquareness of Orlicz-Bochner function spaces equipped with Luxemburg norm are given. We also prove that, in Orlicz-Bochner function spaces generated by locally uniform nonsquare Banach space ...
Cui Yunan +2 more
exaly +6 more sources
Luxemburg Norm Characterizations of BLO Spaces in General Metric Measure Frameworks
MathematicsThis study provides new equivalent descriptions of the Bounded Lower Oscillation (BLO) space through Luxemburg-type Lφ integrability conditions, where φ is a nonnegative function with either convexity or concavity.
Liping Yang, Xin Jiang
exaly +4 more sources
M-constants in Orlicz Spaces Equipped with the Luxemburg Norm
Journal of Harbin University of Science and Technology, 2022 Riesz angle μ2(x)is an important geometric constant in Banach lattice spaces, which is closely related to the fixed point properties of spaces. In this paper, the M-constants of Orlicz function spaces and Orlicz sequence spaces equipped with Luxemburg ...
WANG Zi-xuan, CUI Yun-an, WANG Jing
doaj +2 more sources
Uniformly non-$l_{n}^{(1)}$ Orlicz spaces with Luxemburg norm [PDF]
Studia Mathematica, 1985 It is given a criterion of uniformly non-\(\ell_ n^{(1)}\) Orlicz spaces simpler than one given by \textit{K. Sundaresan} in Isr. J. Math. 3(1965), 139-146 (1966; Zbl 0146.369). This is done in the case of a non-atomic (finite or infinite) as well as of a purely atomic measure.
Henryk Hudzik
exaly +3 more sources
When and where the Orlicz and Luxemburg (quasi-) norms are equivalent?
Journal of Mathematical Analysis and Applications, 2020 Junta de Andalucía FQM ...
Antonio Fernández +2 more
exaly +6 more sources
Monotonicity and best approximation in Orlicz–Sobolev spaces with the Luxemburg norm
Journal of Mathematical Analysis and Applications, 2008 Let \(\Omega\) be a bounded and connected open subset of \(\mathbb{R}^{n}\), and let \((\Omega,\Sigma,\mu)\) be a nonatomic finite measure space. The modular of a measurable function \(u\) on \(\Omega\) is defined by \(\rho_{A}(u)=\int_{\Omega }A(u(t))\,dt\), where \(A(u)\) is a given \(N\)-function. The Orlicz space is \(L_{A}(\Omega )=\{u(t):\) there\
Henryk Hudzik
exaly +3 more sources
Sub Nearly Uniformly Convex of Orlicz Sequence Spaces Equipped with Luxemburg Norm
Journal of Harbin University of Science and Technology, 2022 Nearly uniform noncreasy is a important property in Banach spaces. In this paper we introduce a new geometric property, which is called sub nearly uniformly convex property.
Cui Yun-an, Dai Ming-jun
doaj +2 more sources
Locally Nearly Uniformly Convex Points in Orlicz Spaces Equipped with the Luxemburg Norm
AxiomsThis research explores two novel geometric concepts—nearly convex points and locally nearly uniformly convex points within the frameworks of Banach spaces and Orlicz spaces equipped with the Luxemburg norm.
Yunan Cui, Xiaoxia Wang, Yaoming Niu
doaj +2 more sources
Weighted inequalities and applications to best local approximation in Luxemburg norm
Analysis in Theory and Applications, 2004 The authors use the following notation: \({I_\epsilon:=\{x\in{\mathbb R}^k:\;-\epsilon\leq x_i\leq\epsilon\} }\), \(B_\epsilon\) is the closed ball of radius \(\epsilon\) centered at \(0\), \(\Pi^r\) denotes the set of polynomials of degree at most \(r\). A function \(w\) is a weight function if it is positive a.e.
Cuenya, H. H. +2 more
exaly +2 more sources
Smooth points of Musielak-Orlicz sequence spaces equipped with the Luxemburg norm [PDF]
Colloquium Mathematicum, 1993 The paper gives criteria for smoothness of points in the unit sphere of Musielak-Orlicz sequence spaces. Let \(\varPhi=(\varPhi)_i\) be a Musielak-Orlicz function, \(\ell^{\varPhi}\) the corresponding Musielak-Orlicz sequence space endowed with the Luxemburg norm \(\|.\|\), let \(S(\ell^{\varPhi})\) be the unit sphere in \(\ell^{\varPhi}\), and \(h ...
Henryk Hudzik
exaly +3 more sources