Littlewood-Paley-Stein theory for semigroups in UMD spaces

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The foundational inequalities of D.L. Burkholder and some of their ramifications (2010, background): “We also refer the reader to [28], [72], [90], [91], [92] and [93], which contain many results and further references on singular integrals and other operators with values in Banach spaces with the UMD property and to G.”
γ-Radonifying Operators: A Survey (2010, unknown): “[50] T.P. Hytönen, A. McIntosh, and P. Portal, Kato’s square root problem in Banach spaces, J. Funct.”
Conical square function estimates in UMD Banach spaces and applications to H∞-functional calculi (2007, unknown): “This is done through a linearisation of the square function using randomisation, which gives (see [14]) ∥∥ ∞ 0 t √ ∆e−t √ f dWt √ t ∥∥ L2(Ω;Lp(Rn;X)) h ‖f‖Lp(Rn;X),”