Multipliers and tensor products of weighted Lp-spaces

Özto S., Gürkanli A.

Acta Mathematica Scientia, vol.21, no.1, pp.41-49, 2001 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 1
  • Publication Date: 2001
  • Doi Number: 10.1016/s0252-9602(17)30575-1
  • Journal Name: Acta Mathematica Scientia
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.41-49
  • Keywords: Banach module, Multiplier, Weighted Lp(G) spaces
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

Let G be a locally compact unimodular group with Haar measure rmdx and ω be the Beurling's weight function on G (Reiter, [10]). In this paper the authors define a space Ap,qω (G) and prove that Ap,qω (G) is a translation invariant Banach space. Furthermore the authors discuss inclusion properties and show that if G is a locally compact abelian group then Ap,qω (G) admits an approximate identity bounded in L1ω. (G). It is also proved that the space Lpω (G) ⊗L1ω L̄qω (G) is isometrically isomorphic to the space Ap,qω (G) and the space of multipliers from Lpω (G) to Lq′ω-1 (G) is isometrically isomorphic to the dual of the space Ap,qω (G) iff G satisfies a property Pqp. At the end of this work it is showed that if G is a locally compact abelian group then the space of all multipliers from L1ω (G) to Ap,qω (G) is the space Ap,qω (G).