By Ruilin Long
In the earlier 20 years, the Hp-BMO concept on Rn has passed through a flourishing improvement, which should still in part supply the credits to the applying of a few martin gale inspiration and techniques. it'd be precious to express a few examples pertaining to this aspect. As one of many key components of Calder6n-Zygmund's actual procedure which first seemed within the 50's, Calder6n-Zygmund Decomposition is precisely the so-called preventing time argument in nature which already existed within the chance concept early within the 30's, even though this kind of shut courting among Calder6n-Zygmund De composition and the preventing time argument probably used to be no longer learned consciously at the moment. yet after the 70's we really used the preventing time argument in tentionally as a style of pondering in research. Later, while classical Hp conception had passed through an evolution from one bankruptcy within the advanced Variable thought to an autonomous department (the key step to speed up this evolution was once D. Burkholder R. Gundy-M. Silverstein's recognized paintings within the early 70's at the maximal functionality characterization of Hp), Martingale Hp-BMO conception quickly seemed as a counter a part of the classical Hp-BMO conception. because of the simplicity of the constitution in martingale atmosphere, many new principles and techniques should be produced more straightforward in this degree. those new issues have proven a very good impression at the classical Hp-BMO The ory. for instance, the concept that of atomic decomposition of H P used to be first germinated in martingale environment; the great >.
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