On the weighted variable exponent amalgam space

In [4], a new family of Wiener amalgam spaces was defined and investigated some properties of these spaces, where local component is a variable exponent Lebesgue space Lp(x) (ℝ) and the global component is a weighted Lebesgue space Lqm(ℝ). This present paper is a sequel to our work [4]. In Section 2, we discuss necessary and sufficient conditions for the equality . Later we give some characterization of Wiener amalgam space . In Section 3 we define the Wiener amalgam space and investigate some properties of this space, where FLp(x) is the image of Lp(x) under the Fourier transform. In Section 4, we discuss boundedness of the Hardy-Littlewood maximal operator between some Wiener amalgam spaces.