Geodesic
The diagonal mapping in general Hardy spaces in the polidisk
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 31, Tome 303 (2003), pp. 218-222 
N. A. Chasova; F. A. Shamoyan. The diagonal mapping in general Hardy spaces in the polidisk. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 31, Tome 303 (2003), pp. 218-222. http://geodesic.mathdoc.fr/item/ZNSL_2003_303_a11/
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     title = {The diagonal mapping in general {Hardy} spaces in the polidisk},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

For $p=(p_1,p_2)$, $1, $i=1,2$, let $H^{p_1,p_2}$ be the Hardy class on the bidisk with mixed norm. We give a complete discription of all holomorphic function $\varphi$ in the unit disk that are representable in the form $\varphi(z)=f(z,z)$, $|z|<1$, with $f\in H^{p_1,p_2}$.

[1] Rudin U., Teoriya funktsii v polikruge, Mir, M., 1974 | MR | Zbl

[2] Shamoyan F. A., Chasova N. A., “Opisanie lineinykh nepreryvnykh funktsionalov v prostranstvakh Khardi so smeshannymi normami v polikruge”, Sovremennye metody teorii funktsii i smezhnye voprosy, tezisy dokladov Voronezhskoi zimnei matematicheskoi shkoly, Voronezh, 2001, 285–286

[3] Shamoyan F. A., “Teoremy vlozheniya i kharakteristika sledov v prostranstvakh $H^p (U^n), 0

\infty$”, Mat. sbornik, 107(149):3(11) (1978), 446–462 | MR | Zbl

[4] Tribel X., Teoriya funktsionalnykh prostranstv, Mir, M., 1986 | MR | Zbl

[5] Peller V. V., Khruschev S. V., “Operatory Gankelya, nailuchshie priblizheniya i statsionarnye Gaussovskie protsessy”, Uspekhi mat. nauk, 37:1(223) (1982), 53–124 | MR | Zbl

[6] Djrbashian M. M., Shamoyan F. A., Topics in the theory of $A^p_{\alpha}$ spaces, 105, Teubner-Texte, Leipzig, 1988 | MR | Zbl