Operator-valued Fourier multiplier theorems on Lp(X) and geometry of Banach spaces

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Stochastic Integration in Banach Spaces - a Survey (2013, background): “As a consequence, UMD spaces provide a natural framework for vector-valued harmonic analysis, and indeed large parts of the theory of singular integrals have by now been extended to UMD spaces [6, 40, 42, 45, 69, 98, 101].”
A T1 theorem for integral transformations with operator-valued kernel (2006, background): “An often useful way of thinking of R-boundedness (exploited in [12], [13]) is in terms of the following notion well known from Banach space theory:”
Operator–valued Fourier multiplier theorems on Besov spaces (2003, background): “If X is a subspace of an Lq(Ω) space, then X has Fourier type p = min(q, q′); thus, the l in (1.1) improves (i.e. decreases) as q tends towards 2.”
Fourier embeddings and Mihlin‐type multiplier theorems (2004, methodology): “11 in [8]; we simply apply our new Fourier embeddings instead of the ones used in [8].”