Preface

The acquaintance of a newcomer with real interpolation often starts (and fairly often also finishes) with the Marcinkiewicz theorem about the Lorentz scale L, see, e.g., [SW], [Z], or the introductory material in [BL]. It can be seen from the classical proof that this subtle result is related to careful splitting of a function in two parts. More advanced expositions show (though this may be hidden behind technicalities; see, e.g., [BL] except the introductory material) that, in fact, not too many splittings are required. Specifically, the entire content of the Marcinkiewicz theorem stems from the solution of only one extremal problem.