Geodesic
On the $\Cal L$-characteristic of fractional powers of linear operators
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 1, pp. 21-34.

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We describe the geometric structure of the ${\Cal L}$-characteristic of fractional powers of bounded or compact linear operators over domains with arbitrary measure. The description builds essentially on the Riesz-Thorin and Marcinkiewicz-Stein-Weiss-\linebreak Ovchinnikov interpolation theorems, as well as on the Krasnosel'skij-Krejn factorization theorem.
Classification : 46E30, 46M35, 47A57, 47A60, 47A99, 47B37, 47B38
Keywords: fractional powers of operators; $L$-characteristic; Lebesgue spaces; interpolation theorems 
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Appell, Jürgen; Simões, Marilda A.; Zabrejko, Petr P. On the $\Cal L$-characteristic of fractional powers of linear operators. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 1, pp. 21-34. http://geodesic.mathdoc.fr/item/CMUC_1994__35_1_a2/