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Orlicz Spaces and Generalized Orlicz Spaces

Lecture Notes in Mathematics, 2019
This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak–Orlicz spaces) with minimal assumptions on the generating Φ-function.
Peter Hästö, Petteri Harjulehto
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Orlicz Spaces and Rearranged Maximal Functions

Mathematische Nachrichten, 1987
Given a Young function \(\Phi\) on [0,\(\infty)\), the authors define the \(\Phi\)-mean of the decreasing rearrangement \(f^*\) of some measurable function f by \[ f_{\Phi}^{**}(t)=\inf \{\lambda:\lambda >0,\int^{t}_{0}\Phi (f^*(s)/\lambda)ds\leq t\}; \] if \(\Phi\) is the identity, one gets the usual average rearrangement \(f^{**}\) of f [see e.g ...
Bagby, Richard J., Parsons, John D.
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Distance Functions and Orlicz-Sobolev Spaces

Canadian Journal of Mathematics, 1986
Let ∧ be a bounded, non-empty, open subset of Rn and given any x in Rn, letlet k ∊ N and suppose that p ∞ (1, ∞). It is known (c.f. e.g. [4]) that if u belongs to the Sobolev space WKp(∧) and u/dk ∊ Lp(∧), then . Further results in this direction are given in [5] and [9].
Edmunds, D. E., Edmunds, R. M.
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On the Convexity Coefficient of Musielak–Orlicz Function Spaces Equipped With the Orlicz Norm

Mathematische Nachrichten, 2023
AbstractIn Hudzik and Landes, the convexity coefficient of Musielak–Orlicz function spaces over a non‐atomic measure space equipped with the Luxemburg norm is computed whenever the Musielak–Orlicz functions are strictly convex see [6]. In this paper, we extend this result to the case of Musielak–Orlicz spaces equipped with the Orlicz norm.
Cui Yunan
exaly   +2 more sources

Noncreasy and Uniformly Noncreasy Orlicz Function Spaces

Journal of Mathematical Analysis and Applications, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bor-Luh Lin
exaly   +2 more sources

-convexity of Orlicz–Bochner function spaces endowed with the Orlicz norm

Nonlinear Analysis: Theory, Methods & Applications, 2012
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Shang, Shaoqiang, Cui, Yunan, Fu, Yongqiang   +2 more
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Points of monotonicity in Musielak--Orlicz function spaces endowed with the Orlicz norm

Publicationes Mathematicae Debrecen, 2002
Let \((X,\|\cdot\|,\leq)\) be a Banach lattice, let \(X^+\) denote the positive cone in \(X\) and let \(S(X)\) be the unit sphere of \(X\). A point \(x\in S(X^+)\) is said to be upper (lower) monotone if for any \(y\in X^+\backslash\{0\},\) (any \(y\in X^+\backslash \{0\}, y\leq x)\) there holds \(\|x+y\|>1,(\|x-y\|
Hudzik, H., Liu, Xin Bo, Wang, T.
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On Triple Sequence Spaces of Bernstein Operator of χ3 of Rough λ-Statistical Convergence in Probability of Random Variables Defined by Musielak-Orlicz Function

International Journal of Open Problems in Computer Science and Mathematics, 2018
We introduced the triple sequence spaces of Bernstein polynomials of χ 3 of rough λ − statistical convergence in probability of random variables and discuss general properties of among these sequence spaces defined by Musielak-Orlicz ...
A. Esi, N. Subramanian
semanticscholar   +1 more source

The Bochner Integral of Functions with Values in an Orlicz Space

Southeast Asian Bulletin of Mathematics, 2000
Some properties of Denjoy-Dunford and Denjoy-Pettis Banach-valued integrable functions are obtained. Some results of R. A. Gordon (1989) and J. L. Gamez and J. Mendoza (1998) are generalized. Furthermore, some convergence theorems for these types of integrable functions are obtained.
Navarro, Milagros P., Zheng, Qi
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Points of monotonicity in Orlicz–Lorentz function spaces

Nonlinear Analysis: Theory, Methods & Applications, 2010
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Gong, Wanzhong, Shi, Zhongrui
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