Mixed atomic decomposition of martingale weak

Hardy–Morrey spaces

Lin Yu a, b , ∗ , Xiao Yu c

a School of Science, China Three Gorges University, Yichang, 443002, China

b Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, 443002, China

c System Design Institute of Hubei Aerospace Technology Academy, Wuhan, 430040, China

Abstract

The so-called mixed-type atomic decomposition theorems are established for martingale weak Hardy–Morrey spaces wHM s p ,φ , wHM∗p ,φand wHM s p ,φ , respectively. As applications, a sufficient condition for sublinear operators on martingale weak Hardy–Morrey spaces to be bounded is given. In particular, some classical martingale inequalities, including Burkholder’s inequality, are extended to the case of the weak Morrey space quasi-norms.

Keywords:

Martingale, Atomic decomposition, Hardy space,Morrey space