Details

Autor(en) / Beteiligte

• Long, Ruilin

Titel

Martingale Spaces and Inequalities [Elektronische Ressource]

Ort / Verlag

Wiesbaden : Vieweg+Teubner Verlag

Erscheinungsjahr

1993

Link zum Volltext

• Volltext

Link zu anderen Inhalten

• Volltext

Beschreibungen/Notizen

• 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 martingale 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 Decomposition 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 intentionally 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. BurkholderR. 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 counterpart 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 Theory. For example, the concept of atomic decomposition of H P was first germinated in martingale setting; the good >