Geodesic
Categories of results in variable Lebesgue spaces theory
Rendiconto della Accademia delle scienze fisiche e matematiche, Série 4, Tome 86 (2019) no. 1, pp. 79-102

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Variable (exponent) Lebesgue spaces represent a relevant research area within the theory of Banach function spaces. Much attention is devoted to look for sufficient conditions on the variable exponent to establish the assertions within the theory. In this Note we try to show the beauty of the research in this field, mainly quoting some known results organized into “categories", each of them characterized by a common typology of conditions on the variable exponent. New results involve the failure of rearrangement-invariant property, the rearrangement of the exponent, and a generalization of a formula known for constant exponents. Riassunto – Gli spazi di Lebesgue con esponente variabile rappresentano un set 
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     title = {Categories of results in variable {Lebesgue} spaces theory},
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Fiorenza, Alberto. Categories of results in variable Lebesgue spaces theory. Rendiconto della Accademia delle scienze fisiche e matematiche, Série 4, Tome 86 (2019) no. 1, pp. 79-102. http://geodesic.mathdoc.fr/item/RASFM_2019_4_86_1_a0/