Weighted variable exponent amalgam spaces W(LP(X),LQW)

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Aydin I., Turan Gürkanli A.

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

  • Publication Type: Article / Article
  • Volume: 47 Issue: 1
  • Publication Date: 2012
  • Doi Number: 10.3336/gm.47.1.14
  • Journal Name: Glasnik Matematicki
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.165-174
  • Keywords: Hardy-Littlewood maximal function, Variable exponent Lebesgue space, Wiener amalgam space
  • Ondokuz Mayıs University Affiliated: No

Abstract

In the present paper a new family of Wiener amalgam spaces W(LP(X),LQW) is defined, with local component which is a variable exponent Lebesgue space LP(X)(ℝn) and the global component is a weighted Lebesgue space LQW(ℝn). We proceed to show that these Wiener amalgam spaces are Banach function spaces. We also present new Hölder-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(LP(X),LQW) into itself.