A note on weighted Sobolev algebras L1ω(ℝd) ∩ Wpk (ℝd)

Güngör N., Səgir B.

Journal of the Ramanujan Mathematical Society, vol.30, no.4, pp.361-373, 2015 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 4
  • Publication Date: 2015
  • Journal Name: Journal of the Ramanujan Mathematical Society
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.361-373
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

Let 1 ≤ p < ∞ and ω be Beurling's weight function on ℝd. In this article, we demonstrate some harmonic properties of Sobolev space Wpk (ℝd) which consists of all functions on ℝd whose weak derivatives up to and including order k belong to Lp(ℝd). Also, we deal with some harmonic properties of intersection space Apk,ω(ℝd) = L1ω(ℝd) ∩ Wpk (ℝd) by aid of Beurling algebra L1ω(ℝd) and Sobolev space Wpk (ℝd). Finally, we research the inclusions and continuous embeddings between the spaces Apk,ω(Ω) where Ω ⊂ ℝd be open set.