Duality of fully measurable grand Lebesgue space
In this paper, we prove a Hölder’s type inequality for fully measurable grand Lebesgue spaces, which involves the notion of fully measurable small Lebesgue spaces. It is proved that these spaces are non-reflexive rearrangement invariant Banach function spaces. Moreover, under certain continuity assu...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2017-04-01
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| Series: | Transactions of A. Razmadze Mathematical Institute |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2346809216300903 |
| Summary: | In this paper, we prove a Hölder’s type inequality for fully measurable grand Lebesgue spaces, which involves the notion of fully measurable small Lebesgue spaces. It is proved that these spaces are non-reflexive rearrangement invariant Banach function spaces. Moreover, under certain continuity assumptions, along with several properties of fully measurable small Lebesgue spaces, we establish Levi’s theorem for monotone convergence and that grand and small spaces are associated to each other. Keywords: Banach function norm, Grand Lebesgue space, Associate space and Levi’s theorem |
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| ISSN: | 2346-8092 |