A T1 theorem for integral transformations with operator-valued kernel

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Maximal Regularity for Non-autonomous Equations with Measurable Dependence on Time (2014, background): “ls of convolution type to the vector-valuedsetting (see [50]). In the casethe singularintegralis of nonconvolution type, the situation is much more complicated. An extensive treatment can be found in [47, 48, 49], where T1-theorems [19] and Tb-theorems [20] have been obtained in an inﬁnite dimension”
Pseudo-Localization of Singular Integrals and Noncommutative Littlewood–Paley Inequalities (2008, methodology): “Nevertheless, we refer to Hytönen and Weis [7] for a more in depth explanation of all the identifications we have done so far.”
Smooth Fourier multipliers on group von Neumann algebras (2010, background): “mal behavior of the constants near the boundary points at 1 and ∞, while our approach does due to our stronger L∞ → BMO estimate. As explained in [65], this is a standard lack of vector-valued theory [10, 38, 89]. Remark 1.11. If k(x,y) ∈ M is given by left multiplication, the eﬀect in T† is that k(”