Glasnik Matematicki, Vol. 47, No. 1 (2012), 165-174.

WEIGHTED VARIABLE EXPONENT AMALGAM SPACES W(L^P(X),L_W^Q)

İsmail Aydin and A. Turan Gürkanli

Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayıs University, 55139, Kurupelit, Samsun, Turkey
e-mail: gurkanli@omu.edu.tr

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)(Rⁿ) and the global component is a weighted Lebesgue space L_w^q(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(L^p(x),L_w^q) into itself.

2010 Mathematics Subject Classification.   42B25,42B35.

Key words and phrases.   Variable exponent Lebesgue space, Hardy-Littlewood maximal function, Wiener amalgam space.

DOI: 10.3336/gm.47.1.14

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