Aspect of invariant properties of Orlicz amalgam spaces with respect to Banach spaces

ARIS B., Öztop S.

Journal of Pseudo-Differential Operators and Applications, cilt.16, sa.2, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 2
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s11868-025-00696-5
  • Dergi Adı: Journal of Pseudo-Differential Operators and Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Anahtar Kelimeler: Affine group, Amalgam spaces, Discrete norms, Doubling weights, Orlicz spaces
  • İstanbul Üniversitesi Adresli: Evet

Özet

Let G be a locally compact group, Φ be a Young function. In this paper, we study the amalgam space W(LΦ,Y) defined on G, where the local component space is the Orlicz space LΦ and the global component is a Banach space Y containing the characteristic function of any compact subset of G. We obtain an equivalent norm on W(LΦ,Y). By using the equivalent norm, we investigate right translation invariance and completeness of the amalgam space W(LΦ,Y) with a non translation invariant space Y, in general. We also present an example of a non translation invariant space Y such that W(LΦ,Y) is right translation invariant in contrast to the literature.