|Universiteit Faculteit FNWI English version||19 januari 2006, e-mail|
Woensdag 8 februari 2006
AbstractVector-valued extensions of the classical Lp-multiplier theorems of Marcinkiewicz ('39), Mikhlin ('56) and others have been established by Bourgain ('86) for an important class of Banach spaces (UMD). Operator-valued extensions obtained in the sixties are valid only for operators acting on a space isomorphic to a Hilbert space.
Very recently Lutz Weis ('01) proved a "non-Hilbertian" operator-valued version of the Mikhlin theorem by using in an essential way the notion of an R-bounded family of operators. At the same time he was able to solve a long-standing problem concerning maximal Lp-regularity for abstract parabolic equations in Banach spaces.
The aim of this talk is to introduce and discuss these results following the approach of Arendt and Bu ('02).