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M-Constants in Orlicz–Lorentz Function Spaces
Mathematische Nachrichten, 2019AbstractIn this paper some lower and upper estimates of M‐constants for Orlicz–Lorentz function spaces for both, the Luxemburg and the Amemiya norms, are given. Since degenerated Orlicz functions φ and degenerated weighted sequences ω are also admitted, this investigations concern the most possible wide class of Orlicz–Lorentz function spaces.
Cui Yunan +2 more
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Kadec-Klee property in Musielak-Orlicz function spaces equipped with the Orlicz norm
Aequationes Mathematicae, 2021Yu-Nan Cui, Li Zhao
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Quasiconvex variational functionals in Orlicz–Sobolev spaces
Annali di Matematica Pura ed Applicata, 2011The 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, 2011Let \(\phi(x,t): \mathbb{R}^N\times [0,\infty)\to [0,\infty)\) 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 +3 more
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Conjugate Functionals and Orlicz Spaces
1985In 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, 1996The 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
2007In 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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On Hardy ‐ Littlewood Maximal Functions in Orlicz Spaces
Mathematische Nachrichten, 1997AbstractLet Φ(t) and Ψ(t) be the functions having the following representations Φ(t) = ∫a(s)ds and Ψ(t) = ∫b(s) ds, where a(s) is a positive continuous function such that ∫a(s)/s ds = + ∞ and b(s) is an increasing function such that lims→ ∞ b(s) = + ∞. Then the following statements for the Hardy ‐ Littlewood maximal function M f (x) are equivalent: (i)
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Uniform rotundity of Orlicz function spaces equipped with the p ‐Amemiya norm
, 2018Radosław Kaczmarek
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