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.
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Chao, J.A., Long, R.L. Martingale transforms and Hardy spaces. Probab. Th. Rel. Fields 91, 399–404 (1992). https://doi.org/10.1007/BF01192064
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DOI: https://doi.org/10.1007/BF01192064