Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 535-549

BOUNDEDNESS OF THE MAXIMAL OPERATOR AND ITS COMMUTATORS ON VANISHING GENERALIZED ORLICZ-MORREY SPACES

Fatih Deringoz, Vagif S. Guliyev and Stefan Samko

Ahi Evran University, Department of Mathematics
Bagbasi Campus, 40100, Kirsehir, Turkey; fderingoz 'at' ahievran.edu.tr

Ahi Evran University, Department of Mathematics
Bagbasi Campus, 40100, Kirsehir, Turkey, and
Institute of Mathematics and Mechanics
B. Vahabzade 9, AZ1141, Baku, Azerbaijan; vagif 'at' guliyev.com

Universidade do Algarve, Departamento de Matemática
Campus de Gambelas, 8005-139 Faro, Portugal; ssamko 'at' ualg.pt

Abstract. We prove the boundedness of the Hardy-Littlewood maximal operator and their commutators with BMO-coefficients in vanishing generalized Orlicz-Morrey spaces VMΦ,φ(Rn) including weak versions of these spaces. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness not in integral terms but in less restrictive terms of supremal operators involving the Young function Φ(u) and the function φ(x,r) defining the space. No kind of monotonicity condition on φ(x,r) in r is imposed.

2010 Mathematics Subject Classification: Primary 42B20, 42B25, 42B35, 46E30.

Key words: Vanishing generalized Orlicz-Morrey space, Hardy-Littlewood maximal operator, singular integral operators, commutator, BMO.

Reference to this article: F. Deringoz, V.S. Guliyev and S. Samko: Boundedness of the maximal operator and its commutators on vanishing generalized Orlicz-Morrey spaces. Ann. Acad. Sci. Fenn. Math. 40 (2015), 535-549.

Full document as PDF file

doi:10.5186/aasfm.2015.4029

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