## 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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