Lebesgue and Sobolev spaces with variable exponents

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Traces for fractional Sobolev spaces with variable exponents (2017, unknown): “Introduction We begin this article remembering the definition of the variable exponents Lebesgue space, to this end we follow [4].”
Global gradient estimates for the $p(\cdot)$-Laplacian (2013, methodology): “4 of [9], which proves the same result under the condition f ∈ Lp(·) + L∞.”
A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, methodology): “Variable exponent spaces are carefully treated in the monographs by Cruz-Uribe and Fiorenza [67] and Diening, Harjulehto, Hästö, and Ružička [74].”
Generalized Orlicz spaces and related PDE (2016, background): “The special case φ(x, t) := t, so-called variable exponent spaces L, and corresponding differential equations with non-standard grow th have been vigorously studied in recent years [10, 11, 17].”
Extrapolation and weighted norm inequalities in the variable Lebesgue spaces (2014, background): “By a very deep result of Diening [22, 23], if 1 < p− ≤ p+ < ∞, M is bounded on L if and only if it is bounded on L ′(·).”
Monotone operator theory for unsteady problems in variable exponent spaces (2012, background): “For an extensive presentation we also refer to [14,26].”
Nonlinear parabolic problems in Musielak--Orlicz spaces (2013, background): “For more details on the appearance of this condition in the theory of variable exponent spaces we refer the reader to [10].”