Abstract
The purpose of this article is to survey some recent extensions of the Marcinkiewicz interpolation theorem due to C. Bennett — K. Rudnick and R.A. DeVore — S.D. Riemenschneider — R.C. Sharpley. These results are based on the observation that existing definitions of weak-type operators are somewhat inadequate and that a more natural definition is obtained by considering those operators that are dominated by the Calderon operator Sσ. Since the corresponding interpolation theorems can be lifted into a general Banach space context, this approach has important applications not only in harmonic analysis but in other areas such as approximation theory as well.
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