Original scientific paper

https://doi.org/10.3336/gm.47.1.14

Weighted variable exponent amalgam spaces W(L^p(x),L_w^q)

İsmail Aydin ; Department of Mathematics, Faculty of Arts and Sciences, Sinop University, 57000, Sinop, Turkey
A. Turan Gürkanli ; Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayıs University, 55139, Kurupelit, Samsun, Turkey

Abstract

In the present paper a new family of Wiener amalgam spaces W(Lp(x),Lwq) is defined, with local component which is a variable exponent Lebesgue space Lp(x)(Rn) and the global component is a weighted Lebesgue space Lwq(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),Lwq) into itself.

Keywords

Variable exponent Lebesgue space; Hardy-Littlewood maximal function; Wiener amalgam space

Hrčak ID:

82580

URI

https://hrcak.srce.hr/82580

Publication date:

3.6.2012.

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