The Marcinkievicz Interpolation Theorem for Rearrangement-Invariant Function Spaces and Applications

  • Franziska Fehér

    Rheinisch-Westfälische Technische Hochschule Aachen, Germany

Abstract

The interpolation theorem of J. Marcinkievicz [17] states that any sublinear operator which is simultaneously of weak types () and () is also a bounded operator from the Lebesgue space , into itself, provided . The aim of this paper is to generalize this theorem to the setting of rearrangement-invariant Banach function spaces, and thus to render the theorem available to a much larger range of applications.

Cite this article

Franziska Fehér, The Marcinkievicz Interpolation Theorem for Rearrangement-Invariant Function Spaces and Applications. Z. Anal. Anwend. 2 (1983), no. 2, pp. 111–125

DOI 10.4171/ZAA/53