In the past twenty years the Hp-BMO Theory on Rn has undergone a flourishing development
which should partly give the credit to the application of some martin gale idea and methods. It
would be valuable to exhibit some examples concerning this point. As one of the key parts of
Calder6n-Zygmund's real method which first appeared in the 50's Calder6n-Zygmund Decomposition
is exactly the so-called stopping time argument in nature which already existed in the
Probability Theory early in the 30's although such a close relationship between
Calder6n-Zygmund De composition and the stopping time argument perhaps was not realized
consciously at that time. But after the 70's we actually used the stopping time argument in
tentionally as a method of thinking in Analysis. Later when classical Hp Theory had undergone
an evolution from one chapter in the Complex Variable Theory to an independent branch (the key
step to accelerate this evolution was D. Burkholder R. Gundy-M. Silverstein's well-known work
in the early 70's on the maximal function characterization of Hp) Martingale Hp-BMO Theory
soon appeared as a counter part of the classical Hp-BMO Theory. Owing to the simplicity of the
structure in martingale setting many new ideas and methods might be produced easier on this
stage. These new things have shown a great effect on the classical Hp-BMO The ory. For example
the concept of atomic decomposition of H P was first germinated in martingale setting the good
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