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Schauder decompositions and multiplier theorems. (English) Zbl 0955.46004

The authors study a property called \(R\)-boundedness of a set of operators on a complex Banach space \(E\), showing how this property combines with that of a certain sequence of projections on \(E\) called a Schauder decomposition to yield several Marcinkiewicz-type (vector valued) multiplier theorems.

MSC:

46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
46E40 Spaces of vector- and operator-valued functions
42A45 Multipliers in one variable harmonic analysis
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