“…To see a more detailed history of such spaces see, e.g., [17, §1.1]. These variable exponent function spaces have a wide variety of applications, e.g., in the modeling of electrorheological fluids [4,5,31] as well as thermorheological fluids [6], in the study of image processing [1,2,10,11,14,15,34] and in differential equations with non-standard growth [23,28]. For details on variable Lebesgue spaces one can refer to [16,17,21,27,30] and the references therein.…”