Packing constant in Orlicz spaces equipped with the Luxemburg norm. (English) Zbl 0848.46017
For a given Lebesgue measure space \((T, \Sigma, \mu)\) and Orlicz function \(\Phi\), the authors consider the functional \(I_\Phi\) and Orlicz space \(L^\Phi (\mu)\) with Luxemburg norm \(|\cdot |_\Phi\) (and \(\ell^\Phi\), respectively). This paper contains the formulas for lower and upper bounds for \(D(\ell^\Phi)\) and also for the packing constant \(\Lambda (\ell^\Phi)\) (Theorem 1 and Corollary 1, respectively). In this paper we have a very valuable estimation, with interesting proof for lower bounds of \(D(L^\Phi (\mu))\).
Reviewer: A.Waszak (Poznań)
MSC:
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
