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Identification of Fully Measurable Grand Lebesgue Spaces
Joint Authors
Anatriello, Giuseppina
Chill, Ralph
Fiorenza, Alberto
Source
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-3, 3 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-10-02
Country of Publication
Egypt
No. of Pages
3
Main Subjects
Abstract EN
We consider the Banach function spaces, called fully measurable grand Lebesgue spaces, associated with the function norm ρ(f)=ess supx∈Xδ(x)ρp(x)(f), where ρp(x) denotes the norm of the Lebesgue space of exponent p(x), and p(·) and δ(·) are measurable functions over a measure space (X,ν), p(x)∈[1,∞], and δ(x)∈(0,1] almost everywhere.
We prove that every such space can be expressed equivalently replacing p(·) and δ(·) with functions defined everywhere on the interval (0,1), decreasing and increasing, respectively (hence the full measurability assumption in the definition does not give an effective generalization with respect to the pointwise monotone assumption and the essential supremum can be replaced with the simple supremum).
In particular, we show that, in the case of bounded p(·), the class of fully measurable Lebesgue spaces coincides with the class of generalized grand Lebesgue spaces introduced by Capone, Formica, and Giova.
American Psychological Association (APA)
Anatriello, Giuseppina& Chill, Ralph& Fiorenza, Alberto. 2017. Identification of Fully Measurable Grand Lebesgue Spaces. Journal of Function Spaces،Vol. 2017, no. 2017, pp.1-3.
https://search.emarefa.net/detail/BIM-1176387
Modern Language Association (MLA)
Anatriello, Giuseppina…[et al.]. Identification of Fully Measurable Grand Lebesgue Spaces. Journal of Function Spaces No. 2017 (2017), pp.1-3.
https://search.emarefa.net/detail/BIM-1176387
American Medical Association (AMA)
Anatriello, Giuseppina& Chill, Ralph& Fiorenza, Alberto. Identification of Fully Measurable Grand Lebesgue Spaces. Journal of Function Spaces. 2017. Vol. 2017, no. 2017, pp.1-3.
https://search.emarefa.net/detail/BIM-1176387
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1176387