Infimal convolution and Muckenhoupt Ap(.) condition in variable Lp spaces

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Commutators of fractional integrals on Lebesgue and Herz spaces with variable exponent (2010, background): “The following are the key lemmas due to the author [11, Lemmas 1, 2 and 3]. Lemma 2 has been also considered by Diening [7] and Kopaliani [ 13 ].”
The maximal operator on weighted variable Lebesgue spaces (2011, background): “It has been shown by Kopaliani [29] that condition (1.2) is also sufficient if p is constant outside of a large ball.”