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Weak‐type Fefferman–Stein inequality and commutators on weak Orlicz–Morrey spaces

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  • Ryota Kawasumi

Abstract

We consider the Fefferman–Stein inequality for weak Orlicz–Morrey spaces and the commutators [b,T]$[b,T]$ and [b,Iρ]$[b,I_{\rho }]$ on weak Orlicz–Morrey spaces, where T is a Calderón–Zygmund operator, Iρ$I_{\rho }$ is a generalized fractional integral operator and b is a function in generalized Campanato spaces. We give a necessary and sufficient condition for the boundedness from of [b,T]$[b,T]$ and [b,Iρ]$[b,I_{\rho }]$ from a weak Orlicz Morrey space to another weak Orlicz–Morrey space. We use the Fefferman–Stein inequality to prove the boundedness of the commutators. Since weak Orlicz–Morrey spaces contain the weak Lebesgue, weak Orlicz and weak Morrey spaces as special cases, our results contain the bounedness on these function spaces which are also new results.

Suggested Citation

  • Ryota Kawasumi, 2023. "Weak‐type Fefferman–Stein inequality and commutators on weak Orlicz–Morrey spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 296(12), pages 5356-5383, December.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:12:p:5356-5383
    DOI: 10.1002/mana.202100581
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    References listed on IDEAS

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    1. Yiyu Liang & Dachun Yang & Renjin Jiang, 2016. "Weak Musielak–Orlicz Hardy spaces and applications," Mathematische Nachrichten, Wiley Blackwell, vol. 289(5-6), pages 634-677, April.
    2. Hendra Gunawan & Denny I. Hakim & Kevin M. Limanta & Al A. Masta, 2017. "Inclusion properties of generalized Morrey spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 290(2-3), pages 332-340, February.
    3. Yoshihiro Sawano & Saad R. El†Shabrawy, 2018. "Weak Morrey spaces with applications," Mathematische Nachrichten, Wiley Blackwell, vol. 291(1), pages 178-186, January.
    4. Ryota Kawasumi & Eiichi Nakai & Minglei Shi, 2023. "Characterization of the boundedness of generalized fractional integral and maximal operators on Orlicz–Morrey and weak Orlicz–Morrey spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 296(4), pages 1483-1503, April.
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