Multipliers on some weighted Lp-spaces

Abstract

Let G be a locally compact abelian group with Haar measure dx, and let ω be a symmetric Beurling weight function on G (Reiter, 1968). In this paper, using the relations between pi and qi, where 1<pi,   qi<∞,pi≠qi(i=1,2), we show that the space of multipliers from Lωp(G) to the space S(q′1,q′2,ω−1), the space of multipliers from Lωp1(G)∩Lωp2(G) to Lωq(G) and the space of multipliers Lωp1(G)∩Lωp2(G) to S(q′1,q′2,ω−1).