Sharpness of the Calderón-Lozanovskii interpolation construction |
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| Authors: | V. I. Ovchinnikov Ya. I. Popov |
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| Affiliation: | (1) Voronezh State University, Department of Mathematics, Russia |
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| Abstract: | We present a short proof of the sharpness of the Calderón-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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| Keywords: | interpolation spaces between L p spaces Calderón-Lozanovskii construction sharp interpolation theorem |
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