Kuelbs-Steadman spaces with bounded variable exponents

Abstract

Kuelbs-Steadman spaces  are studied with the frame work of Henstock integrable function spaces with  bounded variable exponent. We desribe a relation between the Lebesgue spaces with  bounded variable exponent  and variable Kuelbs-Steadman spaces. Geometrical property of the spaces are studied. Finally we discuss boundedness behaviour of maximal operator on variable Kuelbs-Steadman spaces.