Compact Embeddings of the Spaces Aw,omega p (Rd)

Abstract

For 1 <= p <= infinity, A(w,omega)(p) (R(d)) denotes the space (Banach space) of all functions in L(w)(1) (R(d)) a weighted L(1)-space (Beurling algebra) with Fourier transforms (f) over cap in L(omega)(p) (R(d)) which is equipped with the sum norm

f

(p)(w,omega) =

f

(1,w) +

(f) over cap

(p,omega), where w and omega are Beurling weights on R(d). This space was defined in [5] and generalized in [6]. The present paper is a sequal to these works. In this paper we are going to discuss compact embeddings between the spaces A(w,omega)(p) (R(d)).