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A new class of restricted type spaces
University of Barcelona, Spain.ORCID iD: 0000-0002-7882-4013
2011 (English)In: Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, E-ISSN 1464-3839, Vol. 54, no 3, 749-759 p.Article in journal (Refereed) Published
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Abstract [en]

We find new properties for the space R(X), introduced by Soria in the study of the best constant for the Hardy operator minus the identity. In particular, we characterize when R(X) coincides with the minimal Lorentz space Λ(X). The condition that R(X) ≠ {0} is also described in terms of the embedding (L1, ∞ ∩ L∞) ⊂ X. Finally, we also show the existence of a minimal rearrangement-invariant Banach function space (RIBFS) X among those for which R(X) ≠ {0} (which is the RIBFS envelope of the quasi-Banach space L1, ∞ ∩ L∞).

Place, publisher, year, edition, pages
2011. Vol. 54, no 3, 749-759 p.
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:su:diva-126111DOI: 10.1017/S0013091509001710OAI: oai:DiVA.org:su-126111DiVA: diva2:897270
Available from: 2016-01-25 Created: 2016-01-25 Last updated: 2017-03-23Bibliographically approved

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