Square functions, bounded analytic semigroups, and applications

Volume 75 / 2007

Christian Le Merdy Banach Center Publications 75 (2007), 191-220 MSC: 47A60, 47D03. DOI: 10.4064/bc75-0-12


To any bounded analytic semigroup on Hilbert space or on $L^p$-space, one may associate natural `square functions'. In this survey paper, we review old and recent results on these square functions, as well as some extensions to various classes of Banach spaces, including noncommutative $L^p$-spaces, Banach lattices, and their subspaces. We give some applications to $H^\infty$ functional calculus, similarity problems, multiplier theory, and control theory.


  • Christian Le MerdyDépartement de Mathématiques
    Université de Franche-Comté
    25030 Besançon Cedex

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