Orlicz amalgam spaces and banach algebra structure

ARIS B., Öztop S.

Monatshefte fur Mathematik, cilt.208, sa.2, ss.221-254, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 208 Sayı: 2
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s00605-025-02118-6
  • Dergi Adı: Monatshefte fur Mathematik
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.221-254
  • Anahtar Kelimeler: Amalgam spaces, Approximate identity, Banach algebra, Convolution, Discrete norms, Locally compact group, Orlicz spaces
  • İstanbul Üniversitesi Adresli: Evet

Özet

Let G be a locally compact group, Φ1,Φ2 be Young functions and ω be a moderate weight function on G. We introduce the weighted Orlicz amalgam spaces W(LΦ1(G),LωΦ2(G)) defined on G, where the local component space is the Orlicz space LΦ1(G) and the global component is the weighted Orlicz space LωΦ2(G). We derive some properties of the spaces W(LΦ1(G),LωΦ2(G)) such as translation invariance, density and duality. We obtain an equivalent discrete type norm on W(LΦ1(G),LωΦ2(G)). By using the equivalent norm, we characterize the Banach algebra W(LΦ1(G),LωΦ2(G)) with respect to convolution when the underlying group is an IN group. We show that W(LΦ1(G),LωΦ2(G)) admits no bounded approximate identity under certain conditions.