Results 151 to 160 of about 344 (181)

-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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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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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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Strongly Extreme Points in Orlicz–Lorentz Function Space Equipped with the Orlicz Norm

The Journal of Geometric Analysis, 2023
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Di Wang, Yunan Cui
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Sobolev’s Inequality for Musielak–Orlicz–Sobolev Functions

Results in Mathematics, 2023
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Yoshihiro Mizuta, Takao Ohno, Tetsu Shimomura   +2 more
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Pointwise behaviour of Orlicz–Sobolev functions

Annali di Matematica Pura ed Applicata, 2008
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Orlicz spaces of essentially bounded functions and Banach-Orlicz algebras

Archiv der Mathematik, 1985
There are characterized all pairs [\(\Phi\),\(\mu\) ], where \(\Phi\) is a convex Orlicz function and \(\mu\) is a \(\sigma\)-finite, positive measure, for which \(L^{\Phi}(\mu)=L^{\infty}(\mu)\) and all these pairs that \(L^{\Phi}(\mu)\) are Banach quasi-algebras (or Banach algebras) under pointwise multiplication of functions.
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Complex rotundity of Musielak--Orlicz function spaces equipped with the Orlicz norm

Publicationes Mathematicae Debrecen, 2004
The authors study some aspects of the geometric theory of Musielak--Orlicz spaces. They prove in Musielak--Orlicz function spaces \(L^0_M\) equipped with the Orlicz norm some criteria for complex extreme points, complex local uniform rotundity, complex uniform rotundity and complex rotundity.
Hao, Cuixia, Liu, Lifang, Fang, Tingfu
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Some inequalities for functions having Orlicz-convexity

Applied Mathematics and Computation, 2016
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Gabriela Cristescu, Muhammad Aslam Noor, Khalida Inayat Noor, Muhammad Uzair Awan   +3 more
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