Abstract
We introduce a new class of rearrangement invariant spaces on the segment [0, 1] which contains the most common extrapolation spaces with respect to the Lp-scale as p → ∞. We characterize the class and demonstrate under certain conditions that the Peetre Open image in new window -functional has extrapolatory description in the couple (E, L∞) if and only if E belongs to the class. By way of application, we establish a new extrapolation theorem for the bounded operators in Lp.
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