Fractional integrals and their commutators on martingale Orlicz spaces
Fractional integrals and their commutators on martingale Orlicz spaces
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DOI：
10.1016/j.jmaa.2020.123991
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发表时间：
2020-07
影响因子：
1.3
通讯作者：
Ryutaro Arai;E. Nakai;Gaku Sadasue
中科院分区：
文献类型：
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作者：
Ryutaro Arai;E. Nakai;Gaku Sadasue
在并矢鞅上，Chao和Ombe（1985）证明了分数阶积分I α及其对易子[b， I α]的L -L - q有界性，其中b在BMO或Lipschitz空间中。我们将这些结果推广到广义分数阶积分I γ及其对位子[b， I γ]的L Φ-L Ψ有界性，其中L Φ和L Ψ是Orlicz空间，而b是广义鞅Campanato空间中更一般的鞅。我们还证明了[b， I γ]的L Φ-F L Ψ φ的有界性，其中F L Ψ φ是triiebel - lizorkin - orlicz空间。此外，我们对b进行了刻画，使得换向子是有界的或紧的。
On the dyadic martingales, Chao and Ombe (1985) proved the L p-L q boundedness of the fractional integrals I α and their commutators [b, I α], where b is in BMO or Lipschitz spaces. We extend these results to L Φ-L Ψ boundedness of generalized fractional integrals I γ and their commutators [b, I γ], where L Φ and L Ψ are Orlicz spaces and b is in generalized martingale Campanato spaces on more general martingales. We also prove the L Φ-F L Ψ ϕ boundedness of [b, I γ], where F L Ψ ϕ is the Triebel-Lizorkin-Orlicz space. Moreover, we characterize b such that the commutator is bounded or compact.