Martingale transforms and Hardy spaces (Q1182502)

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 \(0<p<\infty\), a martingale in \({\mathbf h}^ p\), defined by the conditioned square function, is the martingale transform of a \(\hbox{bmo}_ 2\) martingale with a multiplier sequence whose maximal function is in \(L^ p\).