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On some inequalities in holomorphic function theory in polydisk related to diagonal mapping
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 2, pp. 351-370 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We present a description of the diagonal of several spaces in the polydisk. We also generalize some previously known contentions and obtain some new assertions on the diagonal map using maximal functions and vector valued embedding theorems, and integral representations based on finite Blaschke products. All our results were previously known in the unit disk.
We present a description of the diagonal of several spaces in the polydisk. We also generalize some previously known contentions and obtain some new assertions on the diagonal map using maximal functions and vector valued embedding theorems, and integral representations based on finite Blaschke products. All our results were previously known in the unit disk.
Classification : 32A18
Keywords: polydisk; diagonal mapping; Hardy classes; holomorphic spaces 
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Shamoyan, Romi F.; Mihić, Olivera R. On some inequalities in holomorphic function theory in polydisk related to diagonal mapping. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 2, pp. 351-370. http://geodesic.mathdoc.fr/item/CMJ_2010_60_2_a4/

[1] Aleksandrov, A. V.: Essays on non locally convex Hardy classes. Lecture notes in Mathematics. Springer-Verlag, Complex Analysis and spectral theory V. V. Havin and N. K. Nikolski (1981), 1-99. | DOI | MR

[2] Amar, E., Menini, C.: A counterexample to the corona theorem for operators on $H^2(D^n)$. Pacific J. Math. 206 (2002), 257-268. | MR

[3] Clark, D.: Restrictions of $H^p$ functions in the polydisk. Amer. J. Math. 110 (1988), 1119-1152. | DOI | MR

[4] Coifman, R., Meyer, Y., Stein, E.: Some new functional spaces and their applications to harmonic analysis. J. Funct. Anal. 62 (1985), 304-335. | DOI | MR

[5] Djrbashian, A. E., Shamoyan, F. A.: Topics in the Theory of $A^p_{\alpha}$ Spaces. Leipzig, Teubner (1988). | MR | Zbl

[6] Duren, P. L., Shields, A. L.: Restriction of $H^p$ functions on the diagonal of the polydisk. Duke Math. J. 42 (1975), 751-753. | DOI | MR

[7] Grafakos, L.: Classical and modern Fourier analysis. Prentice Hall (2004). | MR | Zbl

[8] Jevtic, M., Pavlovic, M., Shamoyan, R.: A note on diagonal mapping theorem in spaces of analytic functions in the unit polydisk. Publ. Math. Debrecen 74/1-2 (2009), 1-14. | MR

[9] Mazya, V.: Sobolev Spaces. Springer-Verlag, New York (1985). | MR

[10] Ren, G., Shi, J.: The diagonal mapping in mixed norm spaces. Studia Math. 2 (2004), 103-117. | DOI | MR | Zbl

[11] Rudin, W.: Function theory in polydisks. Benjamin, New York (1969). | MR

[12] Shamoian, F. A.: Embedding theorems and characterization of traces in the spaces $H^p(U^n),$ $p\in (0,\infty)$. Mat. Sbornik, Russian 3 (1978), 709-725.

[13] Shamoian, F. A.: Diagonal mapping and questions of representations in spaces of holomorphic functions in polydisk. Siberian Math. J. Russian 31 (1990), 197-215. | MR

[14] Shamoyan, R. F.: On the action of Hankel operators in bidisk and subspaces in $H^{\infty}$ connected with inner functions in the unit disk. Doklady BAN, Bulgaria 60 (2007), 929-934. | MR | Zbl

[15] Seneta, E.: Regularly varying functions. Springer-Verlag, New York (1976). | MR | Zbl

[16] Shapiro, J.: Mackey topologies, reproducing kernels and diagonal maps on the Hardy and Bergman spaces. Duke Math. J. 43 (1976), 187-202. | DOI | MR

[17] Li, Songxiao, Shamoyan, R. F.: On some properties of a differential operator on the polydisk. Banach J. Math. Anal. (2009), 68-84. | MR

[18] Verbitsky, I.: Multipliers in spaces with fractional norms and inner functions. Siberian Math. J. Russian 150 (1985), 51-72. | MR