Mathematical Researches

Suppose that χ is a Banach function space in the measure space (Ω,A,μ), Φ is an N-function and w is a weight function on Ω. In this article, the Theorem of interpolation in Lebesgue spaces to the weighted generalized Orlicz spaces χΦw corresponding to the Banach function space χ is explained. This Theorem is a generalization of corresponding Theorem in weighted Labesgue and Orlicz spaces. Also, results are presented about the relationship between generalized Orlicz spaces and intermediate spaces, as well as Caldern's product space in weighted generalized Orlicz spaces χΦw.