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Orlicz-Pettis topologies in function spaces

, 1979
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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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M‐constants in Orlicz–Lorentz function spaces

Mathematische Nachrichten, 2019
AbstractIn 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, Foralewski, Paweł, Hudzik, Henryk   +2 more
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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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-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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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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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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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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Noncreasy and uniformly noncreasy Orlicz–Bochner function spaces

Nonlinear Analysis: Theory, Methods & Applications, 2011
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Shi, Zhongrui, Liu, Chunyan
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