SOME ASPECTS OF L-v(q) (R-d) boolean AND W-k(p,w) (R-d)

Gungor N., Sağır Duyar B.

MISKOLC MATHEMATICAL NOTES, vol.16, no.1, pp.165-180, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 1
  • Publication Date: 2015
  • Doi Number: 10.18514/mmn.2015.766
  • Journal Name: MISKOLC MATHEMATICAL NOTES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.165-180
  • Keywords: weighted Sobolev space, Banach module, Banach algebra, approximate identity, continuous embedding, multiplier
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

Let 1 <= q; p < infinity and v,w be Beurling's weight functions on R-d. In this article we deal with harmonic properties of intersection space A(k,v,w)(q,p) (R-d) = L-v(q) (R-d) boolean AND W-k(p,w) (R-d) defined by aid of weighted Lebesgue space L-v(q) (R-d) and weighted Sobolev space W-k(p,w) (R-d). We research the inclusions and inequalities between the spaces A(k,v,w)(q,p) (Omega) where Omega subset of R-d be an open set. Finally, we proved that the spaces M (A(k,w)(1,p) (R-d), L-w(1) (R-d)) can be identified with the weighted spaces of bounded measures M-w (R-d).