Tuomas Hytönen is Professor at the University of Helsinki. A leading expert in Harmonic Analysis with over 60 research papers, he was educated at Helsinki University of Technology and spent a postdoc year at Delft University of Technology. He received a European Research Council Starting Grant in 2011 and gave an invited address to the International Congress of Mathematicians in 2014.

Jan van Neerven is Professor of Analysis at Delft University of Technology. Author of more than 100 research papers and two monographs, he is a leading expert in Operator Theory and Stochastic Analysis. He held post-doctoral positions at Caltech and Tübingen University. He was awarded a Human Capital and Mobility fellowship, a fellowship of the Royal Dutch Academy of Arts and Sciences, and VIDI and VICI subsidies from the Netherlands Organisation for Scientific Research.

Mark Veraar is Associate Professor at Delft University of Technology. Author of over 40 research papers, he is a leading researcher in the theory of evolution equations and stochastic partial differential equations. He held post-doctoral positions at the Universities of Warsaw and Karlsruhe, the latter with a Alexander von Humboldt Fellowship. He is the recipient of VENI and VIDI grants from the Netherlands Organisation for Scientific Research.

Presents a comprehensive and unified account of modern tools for the study of partial differential equations, harmonic analysis, and stochastic analysis in infinite dimensions

Develops a systematic theory of UMD spaces, starting from scratch and reaching substantial Fourier-analytic applications

Offers complete, detailed proofs with explicit bounds for most constants, many of them previously unrecorded in the literature

Includes supplementary material: [...]

1.Bochner Spaces.- 2.Operators on Bochner Spaces.- 3.Martingales.- [...] spaces.- 5. Hilbert transform and Littlewood-Paley Theory.- [...] Problems.- A.Mesaure Theory.- B.Banach Spaces.- C.Interpolation Theory.- D.Schatten classes.