WEIGHTED VARIABLE EXPONENT AMALGAM SPACES W(Lp(x), Lwq)

AYDIN İ., Gurkanli A. T.

GLASNIK MATEMATICKI, vol.47, no.1, pp.165-174, 2012 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 1
  • Publication Date: 2012
  • Journal Name: GLASNIK MATEMATICKI
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.165-174
  • Keywords: Variable exponent Lebesgue space, Hardy-Littlewood maximal function, Wiener amalgam space, LP
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In the present paper a new family of Wiener amalgam spaces W(L-p(x), L-w(q)) is defined, with local component which is a variable exponent Lebesgue space L-p(x)(R-n) and the global component is a weighted Lebesgue space L-w(q) (R-n). We proceed to show that these Wiener amalgam spaces are Banach function spaces. We also present new Holder-type inequalities and embeddings for these spaces. At the end of this paper we show that under some conditions the Hardy-Littlewood maximal function is not mapping the space W(L-p(x), L-w(q)) into itself.