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Literature Cited
A. V. Bukhvalov, “The complex method of interpolation in spaces of vector-valued functions and generalized Besov spaces,” Dokl. Akad. Nauk SSSR,260, No. 2, 265–269 (1981).
A. V. Bukhvalov, “Interpolation of operators in spaces of vector-valued functions with applications to singular integral operators,” Dokl. Akad. Nauk SSSR,278, No. 3, 523–526 (1984).
A. V. Bukhvalov, “Interpolation of generalized Sobolev and Besov spaces with application to the trace theorem for Sobolev spaces,” Dokl. Akad. Nauk SSSR,279, No. 6, 1293–1296 (1984).
A. V. Bukhvalov, “Theorems on interpolation of sublinear operators in spaces with mixed norm,” in: Qualitative and Approximate Methods of Investigating Operator Equations [in Russian], Yaroslavl State Univ. (1984), pp. 90–105.
L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1977).
A. V. Bukhvalov, “Applications of methods of theory of order-bounded operators to the theory of operators in Lp-spaces,” Usp. Mat. Nauk,38, No. 6, 37–83 (1983).
J. Bergh and J. Löfström, Interpolation Spaces, Springer-Verlag, Berlin-New York (1976).
A. P. Calderón, “Intermediate spaces and interpolation, the complex method,” Stud. Math.,24, No. 2, 113–190 (1964).
G. Ya. Lozanovskii, “On certain Banach lattices,” Sib. Mat. Zh.,10, No. 3, 584–599 (1969).
G. Ya. Lozanovskii, “On certain Banach lattices. IV,” Sib. Mat. Zh.,14, No. 1, 140–155 (1973).
G. Ya. Lozanovskii, “On the complex method of interpolation in Banach lattices of measurable functions,” in: Problems of Mathematical Analysis [in Russian], No. 7, Leningrad State Univ. (1979), pp. 83–99.
J. Bergh, “On the relation between the two complex methods of interpolation,” Indiana Univ. Math. J.,28, No. 5, 775–778 (1979).
A. V. Bukhvalov and G. Ya. Lozanovskii, “Sets closed in measure in spaces of measurable functions,” Trudy Mosk. Mat. Obshch.,34, 129–150 (1977).
V. L. Levin, Convex Analysis in Spaces of Measurable Functions and Its Application in Mathematics and Economics [in Russian], Nauka, Moscow (1985).
M. Cwikel, “On (LP0(A0), LP1(A1))θ,q,” Proc. Am. Math. Soc.,44, No. 2, 286–292 (1977).
V. I. Ovchinnikov, “Interpolation theorems that follow from the inequality of Grothendieck,” Funktsional. Anal. Prilozhen.,10, No. 4, 45–54 (1976).
A. V. Bukhvalov, “The Radon-Nikodým property in Banach spaces of measurable vectorvalued functions,” Mat. Zametki,26, No. 6, 875–884 (1979).
A. V. Bukhvalov, “On spaces with mixed norm,” Vestn. Leningr. Gos. Univ., No. 19, 5–12 (1973).
A. V. Bukhvalov, “Integral operators and the representation of completely linear functionals on spaces with mixed norm,” Sib. Mat. Zh.,16, No. 3, 483–493 (1975).
V. A. Shestakov, “Transformations of Banach ideal spaces and interpolation of linear operators,” Bull. Acad. Pol. Sci., Ser. Sci. Math.,29, Nos. 11–12, 569–577 (1981).
V. L. Krepkogorskii, “Two-dimensional K-families,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 12, 67–70 (1982).
Additional information
Leningrad. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 28, No. 1, pp. 37–51, January–February, 1987.
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Bukhvalov, A.V. Interpolation of linear operators in spaces of vector-valued functions and with mixed norm. Sib Math J 28, 24–36 (1987). https://doi.org/10.1007/BF00970205
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DOI: https://doi.org/10.1007/BF00970205