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Zeitschrift für Analysis und ihre Anwendungen


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Volume 2, Issue 2, 1983, pp. 111–125
DOI: 10.4171/ZAA/53

Published online: 1983-04-30

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

Franziska Fehér[1]

(1) Rheinisch-Westfälische Technische Hochschule Aachen, Germany

The interpolation theorem of J. Marcinkievicz [17] states that any sublinear operator $T$ which is simultaneously of weak types ($p_1, q_1$) and ($p_2, q_2$) is also a bounded operator from the Lebesgue space $L_p(0, l), 0 < l \leq \infty$, into itself, provided $p_2 < p < p_1$. 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.

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Fehér Franziska: The Marcinkievicz Interpolation Theorem for Rearrangement-Invariant Function Spaces and Applications. Z. Anal. Anwend. 2 (1983), 111-125. doi: 10.4171/ZAA/53