Results 151 to 160 of about 273 (178)

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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-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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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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Quasiconvex variational functionals in Orlicz–Sobolev spaces

Annali di Matematica Pura ed Applicata, 2011
The paper deals with integral functionals of the form \[ J(u)= \int_\Omega f(\nabla u)\,dx, \] where \(\Omega\) is a domain in \(\mathbb{R}^n\), \(u: \Omega\to\mathbb{R}^N\), and \(f: \mathbb{R}^{nN}\to \mathbb{R}\) is a nonnegative \(C^2\) function.
D. BREIT, VERDE, ANNA
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Capacity for potentials of functions in Musielak–Orlicz spaces

Nonlinear Analysis: Theory, Methods & Applications, 2011
Let \(\phi(x,t): \mathbb{R}^N\times [0,\infty)\to [0,\infty)\) be a convex function of \(x\), satisfying the \(\Delta_2\)-condition for all \(t\geq 0\), defining a Musiełak-Orlicz space \(L^\phi(G)\), \(G\) being an open set in \(\mathbb{R}^N\). The authors define the \((k,\Phi)\)-capacity of \(E\) relative to \(G\), where \(E\subset\mathbb{R}^N\), by ...
Maeda, Fumi-Yuki, Mizuta, Yoshihiro, Ohno, Takao, Shimomura, Tetsu   +3 more
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Conjugate Functionals and Orlicz Spaces

1985
In this chapter, we consider the Orlicz spaces L H and L H* as generalizations of the Lebesgue spaces L p and L q respectively, where p, q > 1, p −1 + q −1 = 1 and explain the connection with conjugate functionals. Orlicz spaces were introduced by Orlicz in 1932.
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Inequalities with weights for maximal functions in orlicz spaces

Acta Mathematica Hungarica, 1996
The author gives conditions for the strong-type modular inequality \[ \int_{\mathbb{R}^n} \Phi (Mf)d\mu\leq \int_{\mathbb{R}^n}\Psi (c|f|)d\mu, \] where \(\Phi\) and \(\Psi\) are Young functions and \(M\) is the Hardy-Littlewood maximal operator.
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DOUBLE SEQUENCE SPACES DEFINED BY ORLICZ FUNCTIONS

2007
In this paper we introduce some new double sequence spaces using the Orlicz function andexamine some properties of the resulting sequence spaces.
Savaş, Ekrem, Patterson, Richard F.
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