On function spaces with wavelet transform in Lpω(ℝd × ℝ+)

Kulak Ö., Gürkanli A. T.

Hacettepe Journal of Mathematics and Statistics, vol.40, no.2, pp.163-177, 2011 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 2
  • Publication Date: 2011
  • Journal Name: Hacettepe Journal of Mathematics and Statistics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.163-177
  • Keywords: Approximate identity, Compact embedding, Essential Banach module, Multipliers space, Wavelet transform
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

Let ω1 and ω2 be weight functions on ℝd, ℝd × ℝ+, respectively. Throughout this paper, we define (ℝd) to be the vector space of f ∈ (ℝd) such that the wavelet transform Wgf belongs to (ℝd × ℝ+) for 1 ≤ p, q < ∞, where 0 6= g ∈ S (ℝd). We endow this space with a sum norm and show that (ℝd) becomes a Banach space. We discuss inclusion properties, and compact embeddings between these spaces and the dual of (ℝd). Later we accept that the variable s in the space (ℝd) is fixed. We denote this space by (ℝd), and show that under suitable conditions (ℝd) is an essential Banach Module over (ℝd). We obtain its approximate identities. At the end of this work we discuss the multipliers from (ℝd) into (ℝd), and from (ℝd) into (ℝd).