Fractional integrals and their commutators on martingale Orlicz spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:487

Article

Arai, Ryutaro¹  Nakai, Eiichi¹  Sadasue, Gaku² 

[1] Ibaraki Univ, Dept Math, Mito, Ibaraki 3108512, Japan

[2] Osaka Kyoiku Univ, Dept Math, Kashiwara, Osaka 5828582, Japan

关键词: Martingale transform;    Fractional integral;    Orlicz space;    Campanato space;    Commutator;   

DOI  :  10.1016/j.jmaa.2020.123991

来源: Elsevier

【 摘 要 】

On the dyadic martingales, Chao and Ombe (1985) proved the L-p-L-q boundedness of the fractional integrals I-alpha and their commutators [b, I-alpha], where bis in BMO or Lipschitz spaces. We extend these results to L-Phi-L-Psi boundedness of generalized fractional integrals I-gamma and their commutators [b, I-gamma], where L-Phi and L-Psi are Orlicz spaces and bis in generalized martingale Campanato spaces on more general martingales. We also prove the L-Phi-F-L Psi(phi) boundedness of [b, I-gamma], where F-L Psi(phi) is the Triebel-Lizorkin-Orlicz space. Moreover, we characterize bsuch that the commutator is bounded or compact. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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