Lebesgue spaces with variable exponents on the p-adic numbers

Variable Lebesgue spaces are a generalization of Lebesgue spaces where we allow the exponent to be a measurable function and thus the exponent may vary. The central topic of this work is to introduce variable exponent Lebesgue spaces where the underlying space is the field of the p-adic numbers and obtain the boundedness of the maximal operator, when the underlying space is a subset of the field of the p-adic numbers which can be bounded or unbounded.}