## Tokyo Journal of Mathematics

### Maximal Operator and its Commutators on Generalized Weighted Orlicz-Morrey Spaces

#### Abstract

In the present paper, we shall give necessary and sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator and its commutators on generalized weighted Orlicz-Morrey spaces $M^{\Phi,\varphi}_{w}({\mathbb R}^n)$. 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 and we do not need $\Delta_2$-condition for the boundedness of the maximal operator. We also consider the vector-valued boundedness of the Hardy-Littlewood maximal operator.

#### Article information

Source
Tokyo J. Math., Volume 41, Number 2 (2018), 347-369.

Dates
First available in Project Euclid: 18 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1513566020

Mathematical Reviews number (MathSciNet)
MR3908799

Zentralblatt MATH identifier
1388.42057

#### Citation

DERINGOZ, Fatih; GULIYEV, Vagif S.; HASANOV, Sabir G. Maximal Operator and its Commutators on Generalized Weighted Orlicz-Morrey Spaces. Tokyo J. Math. 41 (2018), no. 2, 347--369. https://projecteuclid.org/euclid.tjm/1513566020

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