Vector-valuedextentions of some classical theorems in harmonic analysis

Girardi, Maria
Weis, Lutz

facul_01; 34

Abstract:
This paper surveys some recent results
on vector-valued Fourier multiplier theorems
and pseudo differential operators,
which have found important application
in the theory of evolution equations.
The approach used combines methods from Fourier analysis and the
geometry of Banach spaces, such as R-boundedness.

Primary MSC: 42B15 Multipliers, 46E40 Spaces of vector- and operator-valued functions, 46B09 Probabilistic methods in Banach space theory
Secondary MSC: 46B20 Geometry and structure of normed linear spaces, 46E35 Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
Keywords: R-boundedness, Mihlin multiplier theorem,pseudo differential operators,Fourier type, Littlewood-Paley decomposition, vector-valued Besov spaces
Notes:
To appear:
Analysis and Applications - ISAAC 2001,
eds. H.G.W. Begehr, R.P. Gilbert, M.W.Wong.
Kluwer, Dordrecht