Analysis in Banach spaces Tuomas Hytönen Jan van Neerven Mark Veraar Lutz Weis ; volume 3: Harmonic analysis and spectral theory This third volume of Analysis in Banach Spaces offers a systematic treatment of Banach space valued singular integrals Fourier transforms and function spaces. It further develops and ramifies the theory of functional calculus from Volume II and describes applications of these new notions and tools to the problem of maximal regularity of evolution equations. The exposition provides a unified treatment of a large body of results much of which has previously only been available in the form of research papers. Some of the more classical topics are presented in a novel way using modern techniques amenable to a vector valued treatment. Thanks to its accessible style with complete and detailed proofs this book will be an invaluable reference for researchers interested in functional analysis harmonic analysis and the operator theoretic approach to deterministic and stochastic evolution equations. 11 Singular integral operators 12 Dyadic operators and the T (1) theorem 13 The Fourier transform and multipliers 14 Function spaces 15 Bounded imaginary powers 16 The H∞ functional calculus revisited 17 Maximal regularity 18 Nonlinear parabolic evolution equations in critical spaces Appendix Q: Questions Appendix K: Semigroup theory revisited Appendix L: The trace method for real interpolation theory.