$B$值弱Orlicz $\alpha$拟鞅空间的原子分解

Abstract

Abstract:

As we all know, atomic decompositions is a powerful tool for studying martingale space, which can deal with problems concisely and effectively. In this paper, we define several types of weak Orlicz $\alpha$ -quasi-martingale spaces and three types of quasi-atoms, and establish the strong atomic decomposition theorems. By atomic decompositions, we prove the boundedness of sublinear operators on these spaces and the continuous embedding relationship between these spaces.

Key words: Weak Orlicz spaces, $\alpha$ -Quasi-martingale spaces, Atomic decompositions, Sublinear operators

CLC Number:

O211.6

Chuanzhou Zhang,Tiantian Li,Fan Jiao. Atomic Aecompositions of $B$ -Valued Weak Orlicz $\alpha$ -Quasi-Martingale Spaces[J].Acta mathematica scientia,Series A, 2022, 42(1): 9-17.

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References 15

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Atomic Aecompositions of $B$ -Valued Weak Orlicz $\alpha$ -Quasi-Martingale Spaces

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Atomic Aecompositions of BB-Valued Weak Orlicz α\alpha-Quasi-Martingale Spaces

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Atomic Aecompositions of $B$ -Valued Weak Orlicz $\alpha$ -Quasi-Martingale Spaces