Hardy-Littlewood maximal operator on L^p(x) (ℝ)

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Lorentz spaces with variable exponents (2012, background): “The study of the maximal operator in the frame of Lebesgue spaces with variable exponents attracted a lot of attention with the most important breakthroughs being achieved in [8], [9], [11], [13], [27].”
THE HERZ-TYPE HARDY SPACES WITH VARIABLE EXPONENT AND THEIR APPLICATIONS (2012, background): “There exist some sufficient conditions on p(·) such that the maximal operator M is bounded on Lp(·)(Rn), see [1-4, 11, 12].”
On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications (2008, unknown): “But for other, weaker results see [9,24,28].”
An atomic decomposition of variable Besov and Triebel-Lizorkin spaces (2009, background): “Moreover, these spaces have been applied to partial differential equations and the calculus of variation, see [1, 3, 4, 5, 6, 7, 8, 10, 11, 12, 16, 17, 18, 19, 21, 22, 29] and references therein.”