Presents a thorough study of the basic randomisation techniques and the operator-theoretic aspects of the theory.

Offers the first comprehensive treatment of R-boundedness, Banach space-valued square functions and ?-radonifying operators Develops their deep connections with the holomorphic functional calculus of sectorial and bi-sectorial operators Offers a self-contained presentation and complete, detailed proofs of results in both the core and the background material

Autorentext

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 leadingresearcher 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. Lutz Weis, a Professor at Karlsruhe Institute of Technology, is a senior researcher in operator theory and evolution equations. He has published over 80 research papers and a monograph. Since receiving his PhD from University of Bonn, he was a professor at Louisiana State University and visiting professor at TU Berlin as well as Universities of Kiel, South Carolina and Minnesota. He organized a Marie Curie training site and is currently a member of a DFG Graduiertenkolleg.

Inhalt

6.Random sums.-7.Type, cotype, and related properties.- 8.R-boundedness.- 9.Square functions and radonifying operators.- 11.The H1-functional calculus.- P.Open problems.- E.Probability theory.- F Banach lattices.- G Semigroups of linear operators.- H.Holomorphic functions on the strip.- I.Muckenhoupt weights.- References.- Index.