Sobolev Type Spaces Based on Lorentz-Karamata Spaces

Eryılmaz İ.

FILOMAT, vol.30, no.11, pp.3023-3032, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 11
  • Publication Date: 2016
  • Doi Number: 10.2298/fil1611023e
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3023-3032
  • Keywords: Slowly varying function, Lorentz-Karamata space, Sobolev space, FP-algebra, weak factorization, ALGEBRAS, SUBALGEBRAS, EMBEDDINGS
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this paper, firstly Lorentz-Karamata-Sobolev spaces W-L(p,q;b)(k) (R-n) of integer order are introduced and some of their important properties are emphasized. Also, Banach spaces A(L(p,q;b))(k) (R-n) = L-1 (R-n) boolean AND W-L(p,q;b)(k) (R-n) (Lorentz-Karamata-Sobolev algebras) are studied. Using a result of H.C.Wang, it is showed that Banach convolution algebras A(L(p,q;b))(k) (R-n) don't have weak factorization and the multiplier algebra of A(L(p,q;b))(k) (R-n) coincides with the measure algebra M(R-n) for 1 < p < infinity and 1 <= q < infinity.