Abstract
We present a short proof of the sharpness of the Calderon-Lozanovskii interpolation construction in couples of weighted L p spaces in the “lower triangle,” i.e., for operators from a couple { L p0 (V 0), L p1 (V 1)} to a couple {L q0 (U 0), L q1 (U 1)} with p 0 ⩾ q 0 and p 1 ⩾ q 1. This generalizes the well-known result due to Dmitriev and Semenov on the sharpness of the Riesz-Thorin interpolation theorem in the “lower triangle” for L p spaces on intervals.
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