Variable exponent Sobolev spaces on metric measure spaces

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The maximal operator on weighted variable Lebesgue spaces (2011, background): “More general metric measure spaces have been studied for instance in [16, 18, 19, 28, 34]; the discrete weighted case was studied in [36].”
Sobolev's inequalities and vanishing integrability for Riesz potentials of functions in the generalized Lebesgue space Lp(⋅)(logL)q(⋅) (2008, unknown): “8 below) is given in Section 2, which is an extension of Almeida-Samko [3], Diening [6], Futamura-Mizuta [10], Futamura-Mizuta-Shimomura [11, 12], Harjulehto-HästöPere [18], Kokilashvili-Samko [21], Mizuta-Shimomura [27] and Samko-Vakulov [31].”