Atomic decompositions of Lorentz martingale spaces and applications

By Jiao Yong, Peng Lihua, L. Peide. 2009

73 citations recorded by the source corpus.

In the paper we present three atomic decomposition theorems of Lorentz martingale spaces. With the help of atomic decomposition we obtain a sufficient condition for sublinear operator defined on Lorentz martingale spaces to be bounded. Using this sufficient condition, we investigate some inequalities on Lorentz martingale spaces. Finally we discuss the restricted weak-type interpolation, and prove the classical Marcinkiewicz interpolation theorem in the martingale setting.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/187e6027c7e23d85c2d8b83110947207316b25ca

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In Applied Mathematics

1. Yong Jiao
2. Guangheng Xie
3. Dejian Zhou
4. Lian Wu
5. E. Nakai
6. Dachun Yang
7. Yoshihiro Sawano
8. Wen Yuan

In Mathematical Physics

1. Yong Jiao
2. Guangheng Xie
3. Dejian Zhou
4. Lian Wu
5. E. Nakai
6. Dachun Yang
7. Wen Yuan
8. Ciqiang Zhuo

Citations in the corpus

• The predual and John-Nirenberg inequalities on generalized BMO martingale spaces (2014, methodology): “In particular, Jiao, Peng and Liu [11] proved the atomic decompositions of martingale Hardy-Lorentz spaces in 2009.”
• Martingale Orlicz‐Hardy spaces (2012, background): “Martingale Lorentz spaces and martingale Lorentz-Hardy spaces were investigated in [8], [9], [10], etc.”
• DUAL SPACES AND JOHN–NIRENBERG INEQUALITIES OF MARTINGALE HARDY–LORENTZ–KARAMATA SPACES (2015, methodology): “1 in this paper is true for all 0 < p < ∞ and 0 < q ≤ ∞, which improves atomic decomposition theorems in [11, 14, 22].”