Martingale Transforms between Martingale Hardy-amalgam Spaces

Abstract

We discuss martingale transforms between martingale Hardy-amalgam spaces $H_{p,q}^s,Q_{p,q}$ and $P_{p,q}.$ Let and and let $f=\left(f_n,n\in \mathbb{N}\right)$ be a martingale in $P_{p_1,q_1}$; then, we show that its martingale transforms are the martingales in $P_{p,q}$ for some $p,q$ and similarly for $H_{p,q}^s$ and $Q_{p,q}.$