On functions with Fourier transforms in Alipp(G)

Aydin I., Saǧir B.

Demonstratio Mathematica, vol.41, no.2, pp.425-432, 2008 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 2
  • Publication Date: 2008
  • Doi Number: 10.1515/dema-2008-0218
  • Journal Name: Demonstratio Mathematica
  • Journal Indexes: Scopus
  • Page Numbers: pp.425-432
  • Keywords: Fourier transforms, Lipschitz spaces, Multipliers
  • Ondokuz Mayıs University Affiliated: Yes


Let G be a metrizable locally compact Abelian group with dual group Ĝ. For 1 ≤ p < ∞, Ap(G) denotes the vector space of all complex-valued functions in L1(G) whose Fourier transforms f belong to Lp (Ĝ). Research on the spaces Ap(G) was initiated by Warner in [14] and Larsen, Liu and Wang in [7], Martin and Yap in [8]. Let Lip(α,p) and lip(α,p) denote the Lipschitz spaces defined on G. In the present paper, the space Alipp(G) consisting of all complex-valued functions f ∈ lip(α, 1) whose Fourier transforms fbelong to Lp(Ĝ) is investigated. In the first section invariant properties and asymptotic estimates for the translation and modulation operators axe given. Furthermore it is showed that space Alipp(G) is homogeneous Banach space. At the end of this work, it is proved that the space of all multipliers from L1 (G) to Alipp(G) is the space Alipp(G).