Multipliers and tensor products of weighted Lp-spaces

Özto S., Gürkanli A.

Acta Mathematica Scientia, cilt.21, sa.1, ss.41-49, 2001 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Sayı: 1
  • Basım Tarihi: 2001
  • Doi Numarası: 10.1016/s0252-9602(17)30575-1
  • Dergi Adı: Acta Mathematica Scientia
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.41-49
  • Anahtar Kelimeler: Banach module, Multiplier, Weighted Lp(G) spaces
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

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).