Geodesic
Embedding theorems and a characterization of traces in the spaces $H^p(U^n)$, $0$
Sbornik. Mathematics, Tome 35 (1979) no. 5, pp. 709-725 Cet article a éte moissonné depuis la source Math-Net.Ru

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A complete characterization is obtained of the measures $d\mu$ on the unit disk $U$ for which the operator $Df(z)=f(z,z,\dots,z)$ maps $H^p(U^n)$ into $L^p(d\mu)$, $0< p<\infty$. The solution to a problem of W. Rudin is obtained as a corollary. Bibliography: 16 titles. 
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     title = {Embedding theorems and a~characterization of traces in the spaces $H^p(U^n)$, $0<p<\infty$},
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     year = {1979},
     volume = {35},
     number = {5},
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     url = {http://geodesic.mathdoc.fr/item/SM_1979_35_5_a5/}
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F. A. Shamoyan. Embedding theorems and a characterization of traces in the spaces $H^p(U^n)$, $0

[1] L. Hormander, “$L^p$-estimates for (pluri) subharmonic functions”, Math. Scand., 20 (1967), 65–78 | MR

[2] L. Carleson, “Interpolations by bounded analytic functions and the corona problem”, Ann. Math., 76:3 (1962), 547–559 | DOI | MR | Zbl

[3] L. Carleson, “A counter example for measures bounded in $H^p$, for the bidisc”, Institut Mittag-Lefler Report, 1974, no. 7 | Zbl

[4] U. Rudin, Teoriya funktsii v polikruge, izd-vo “Mir”, Moskva, 1974 | MR

[5] M. M. Dzharbashyan, “K probleme predstavimosti analiticheskikh funktsii”, Soobsch. in-ta matem. i mekh. AN Arm. SSR, 1948, no. 2, 3–40

[6] F. A. Shamoyan, “Teorema vlozheniya v prostranstvakh $n$-garmonicheskikh funktsii i nekotorye prilozheniya”, DAN Arm. SSR, LXII:1 (1976), 10–14

[7] P. Duren, A. Shields, “Restrictions $H^p$ functions to the diagonal of the polydisc”, Duke Math. J., 42:4 (1975), 567–579 | DOI | MR

[8] C. Hörowitz and Oberlin, “Restrictions to diagonal of $U^n$”, Indiana Univ. Math. J., 24:7 (1976), 767–772

[9] J. H. Shapiro, “Maccy topologuies, reproducing Kernrls and diagonal maps on the Hardy and Bergman spaces”, Duke Math. J., 43:1 (1976), 187–202 | DOI | MR | Zbl

[10] I. Stein, Singulyarnye integraly i differentsialnye svoistva funktsii, izd-vo “Mir”, Moskva, 1973 | MR

[11] F. A. Shamoyan, “Teoremy vlozheniya, svyazannye s zadachei kratnogo interpolirovaniya v prostranstvakh $U^p$”, Izv. AN Arm. SSR, seriya matem., XI:2 (1976), 124–131

[12] F. A. Shamoyan, “Ob ogranichennosti odnogo klassa operatorov, svyazannykh s delimostyu analiticheskikh funktsii”, Izv. AN Arm. SSR, seriya matem., VIII:6 (1973), 474–490

[13] E. Gagliardo, “Garraterisationi delle trace sulla frantiera relative ad alcune classi di functioni in $n$ variablii”, Rend. Sem. Math. Padova, 27 (1957), 284–305 | MR | Zbl

[14] H. A. Shirokov, “Nekotorye obobscheniya teoremy Littlvuda–Peli”, Zapiski nauchnykh seminarov LOMI, 39 (1974), 162–175 | Zbl

[15] A. Zygmund, “On certain integrals”, Trans. Amer. Math. Soc., 55 (1944), 170–204 | DOI | MR | Zbl

[16] A. Zigmund, Trigonometricheskie ryady, t. 2, izd-vo “Mir”, Moskva, 1965 | MR