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Original scientific paper

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

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page 165-174

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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.


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

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