Sobolev embeddings in metric measure spaces with variable dimension

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Maximal and Potential Operators in Variable Exponent Morrey Spaces (2008, background): “To this end, we first need the estimate given in the following lemma which was obtained in [11] in the framework of general metric measure spaces setting; we give its another proof for the sake of completeness.”
Operators of harmonic analysis in weighted spaces with non-standard growth (2008, methodology): “The non-weighted boundedness of the maximal operator on homogeneous spaces was proved by P.Harjulehto, P.H¨ast¨o and M.Pere [25] and Sobolev embedding theorem with variable exponents on homogeneous spaces with variable dimension was proved in P.Harjulehto, P.H¨ast¨o and V.Latvala [24].”
Sobolev inequalities with variable exponent attaining the values $1$ and $n$ (2008, unknown): “, in [1], [2], [4], [5], [8], [10], [11], [12], [13], [15], [16], [20], [24], [28] in the variable exponent setting.”
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].”