Multipliers and tensor products of weighted L-p-spaces


Oztop S., Gurkanli A.

ACTA MATHEMATICA SCIENTIA, vol.21, no.1, pp.41-49, 2001 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 1
  • Publication Date: 2001
  • Journal Name: ACTA MATHEMATICA SCIENTIA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.41-49
  • Istanbul University Affiliated: Yes

Abstract

Let G be a locally compact unimodular group with Haar measure rmdx and Le be the Beurling's weight function on G (Reiter, [10]). In this paper the authors define a space A(omega)(p,q) (G) and prove that A(omega)(p,q) (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 A(omega)(p,q) (G) admits an approximate identity bounded in L-1 omega (G). It is also proved that the space L-omega(p) (G) x (L1 omega) L-omega(q) (G) is isometrically isomorphic to the space A(omega)(p,q) (G) and the space of multipliers from L-omega(p) (G) to L-omega -1(q') (G) is isometrically isoinorphic to the dual of the space A(omega)(p,q) (G) iff G satisfies a property P-p(q). 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 L-omega(1) (G) to A(omega)(p,q) (G) is the space A(omega)(p,q) (G).