Implementation of the Sparr Interpolation Method in Classes of Spaces of Smooth Functions
Matematičeskie zametki, Tome 70 (2001) no. 4, pp. 581-590.

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The multidimensional Sparr interpolation method is implemented in the Besov spaces $B^s_{p,q}$ and the Lizorkin–Triebel spaces $F^s_{p,q}$. It is shown that this results in Besov spaces of type $B^s_{p,q,(q)}$. An interpolation theorem for Besov spaces using weak conditions of the form $T\colon F^s_{p,1,(1)}\to F^{\widetilde s}_{\widetilde p,\infty,(\infty)}$ is formulated.
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V. L. Kreptogorskii. Implementation of the Sparr Interpolation Method in Classes of Spaces of Smooth Functions. Matematičeskie zametki, Tome 70 (2001) no. 4, pp. 581-590. http://geodesic.mathdoc.fr/item/MZM_2001_70_4_a9/

[1] Sparr G., “Interpolation of several Banach spaces”, Ann. Mat. Pura Appl., 99 (1976), 247–316 | MR

[2] Cobos F., Peetre J., “Interpolation of compact operators: the multidimensional case”, Proc. London Math. Soc. Ser. 3, 63 (1991), 371–400 | DOI | MR | Zbl

[3] Carro M. J., “Real interpolation for families of Banach spaces”, Studia Math., 59:1 (1994), 1–21 | MR

[4] Asekritova I., Krugljak N., “On equivalence of $K$- and $J$-methods for $(n+1)$-tuples of Banach spaces”, Studia Math., 122:2 (1997), 99–115 | MR

[5] Tribel Kh., Teoriya interpolyatsii, funktsionalnye prostranstva, differentsialnye operatory, Mir, M., 1980

[6] Krepkogorskii V. L., “Interpolyatsiya v prostranstvakh Lizorkina–Tribelya i Besova”, Matem. sb., 185:7 (1994), 63–76

[7] Krepkogorskii V. L., “O mnogomernykh metodakh interpolyatsii”, Izv. vuzov. Matem., 1999, no. 11, 41–49 | MR | Zbl

[8] Fernandez D. L., “Interpolation of $2^d$ Banach spaces and the Calderon space $X(E)$”, Proc. London Math. Soc. Ser. 3, 56 (1988), 143–162 | DOI | Zbl