Martingale transforms and Hardy spaces

Summary Burkholder's martingale transforms are especially useful in studying predictable martingale Hardy spaces. Characterizations of such spaces via martingale transforms are provided. In particular, it is shown that for 0<p<, a martingale inh ^p , defined by the conditioned square function, is the martingale transform of a bmo₂ martingale with a multiplier sequence whose maximal function is inL ^p .