English

Certain properties of Generalization of $L^p-$Spaces for $0 < p < 1$

Functional Analysis 2022-05-24 v1

Abstract

This paper introduces the notion of NN^*-function and gives a generalization of Lp,L^p, for 0<p<10<p<1 denoted by LΦL_\Phi where Φ\Phi is an NN^*-function. As well as, this paper examines some properties regarding to this generalized spaces and its linear forms, including some analogies and common features to some other well known spaces. As well as, we prove this space is a quasi-normed space but it is not normed space.

Keywords

Cite

@article{arxiv.2205.10633,
  title  = {Certain properties of Generalization of $L^p-$Spaces for $0 < p < 1$},
  author = {Rabab Elarabi and Mouhssine El-Arabi and Mohamed Rhoudaf},
  journal= {arXiv preprint arXiv:2205.10633},
  year   = {2022}
}