On the weighted variable exponent amalgam space W (Lp(x), Lmq)

In [4], a new family. W (Lp(x),Lmq) 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. W (Lp(x),Lmq)=Lq(ℝ). Later we give some characterization of Wiener amalgam space. W (Lp(x),Lmq). In Section 3 we define the Wiener amalgam space. W (FLp(x),Lmq) 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. © 2014 Wuhan Institute of Physics and Mathematics.