Chapter 6 - Martingales and Singular Integrals in Banach Spaces

By D. Burkholder. 2001

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$H^{\infty }$ functional calculus and square functions on noncommutative $L^p$-spaces (2006, methodology): “We will make use of UMD Banach spaces, for which we refer to [17].”
Continuous local martingales and stochastic integration in UMD Banach spaces (2007, background): “For an overview of the theory of UMD spaces we refer the reader to [4, 24] and references given therein.”
Kato's square root problem in Banach spaces (2007, background): “A recent survey paper on UMD spaces is [14].”
The foundational inequalities of D.L. Burkholder and some of their ramifications (2010, background): “For some of Burkholder’s other contributions to UMD spaces, we refer the reader to [36] and [49].”