Interpolation of operators of weak type between rearrangement invariant function spaces

Abstract

Various types of theorems on interpolation of operators of weak type between L p (0, ∞) spaces can be found in the literature. The more general problem of interpolation between rearrangement invariant spaces is discussed in the present paper. It is proved that if a rearrangement invariant function space X lies, in a certain sense, between the rearrangement invariant spaces X 1 and X 2, then every operator of weak type on X i , i = 1, 2, is a bounded operator on X.