Geodesic
Free multiple interpolation
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 40, Tome 401 (2012), pp. 103-121
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Our aim in this article is to construct a bounded linear operator that solves the problem of multiple interpolation (interpolation with derivatives). It is proved that such an operator exists for nontangential and sparse interpolation sets if we consider interpolation by analytic functions satisfying the following condition: $|f^{(m)}(z_1)-f^{(m)}(z_2)|\leq\omega(|z_1-z_2|)$. 
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A. M. Kotochigov. Free multiple interpolation. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 40, Tome 401 (2012), pp. 103-121. http://geodesic.mathdoc.fr/item/ZNSL_2012_401_a5/

[1] L. Carleson, “An interpolation problem for bounded analytic functions”, Amer. J. Math., 80:4 (1958), 921–930 | DOI | MR | Zbl

[2] A. M. Kotochigov, “Interpolyatsiya analiticheskimi funktsiyami, gladkimi vplot do granitsy”, Zap. nauchn. semin. LOMI, 30, 1972, 167–169 | MR | Zbl

[3] V. I. Vasyunin, “O chisle serii Karlesona”, Zap. nauchn. seminarov LOMI, 65, 1976, 178–182 | MR | Zbl

[4] A. M. Kotochigov, “Svobodnaya interpolyatsiya v klassakh funktsii s $s$-i proizvodnoi iz klassa Khardi”, Zap. nauchn. semin. POMI, 303, 2003, 169–202 | MR | Zbl

[5] A. M. Kotochigov, “Interpolyatsiya v prostranstvakh analiticheskikh funktsii, opredelyaemykh modulem nepreryvnosti”, Teoriya funktsii, funktsionalnyi analiz i ikh prilozheniya, 41, 1983, 77–90

[6] V. K. Dzyadyk, Vvedenie v teoriyu priblizheniya funktsii polinomami, “Nauka”, Moskva, 1977 | Zbl

[7] P. Kusis, Vvedenie v teoriyu prostranstv $H^p$, “Mir”, Moskva, 1984 | MR

[8] G. M. Goluzin, Geometricheskaya teoriya funktsii kompleksnogo peremennogo, “Nauka”, Moskva, 1966 | MR | Zbl