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On Restriction of Weighted Spaces of Holomorphic Functions in the Unit Matrix Disc to the Unit Bidisc

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Abstract

For weighted Lp-spaces of holomorphic functions in the unit matrix disc Rn2 the following problem is investigated: what type of function spaces in the unit bidisc are obtained when the mentioned spaces are restricted to the “diagonal” of the domain Rn2.

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References

  1. M. M. Djrbashian, “On the representability of certain classes of functions meromorphic in the unit disc,” Dokl. Akad. Nauk Arm. SSR 3(1), 3–9 (1945).

    Google Scholar 

  2. M. M. Djrbashian, “On the problem of representability of analytic functions,” Soobshch. Inst. Matem. Mekh. Akad. Nauk Arm. SSR 2, 3–40 (1948) (in Russian).

    Google Scholar 

  3. A. E. Djrbashian and F. A. Shamoyan, Topics in the Theory of A pα Spaces, Vol. 105 of Teubner-Texte zur Math. (Teubner, Leipzig, Germany, 1988).

    Google Scholar 

  4. F. Forelli and W. Rudin, “Projections on spaces of holomorphic functions in balls,” Ind. Univ. Math. J. 24, 593–602 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  5. W. Rudin, Function Theory in the Unit Ball of C n (Springer, Berlin, Heidelberg, New York, 1980).

    Book  MATH  Google Scholar 

  6. M. M. Djrbashian, “Survey of some achievements of Armenian mathematicians in the theory of integral representations and factorization of analytic functions,” Mat. Vesn. 39, 263–282 (1987).

    MathSciNet  Google Scholar 

  7. M. M. Djrbashian, “A brief survey of the results obtained by Armenian mathematicians in the field of factorization theory of meromorohic functions and its applications,” J. Contemp. Math. Anal. 23(6), 8–34 (1988).

    Google Scholar 

  8. L. K. Hua, Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains, Vol. 6 of Translations of Mathematical Monographs (Am. Math. Soc., Providence, RI, 1963).

    Book  Google Scholar 

  9. M. M. Djrbashian and A. H. Karapetyan, “Integral representations in a generalized unit disc,” J. Contemp. Math. Anal. 24(6), 1–25 (1989); Sov. Math. Dokl. 41, 400–403 (1990).

    MathSciNet  Google Scholar 

  10. A. H. Karapetyan, “Bounded projections in weighted function spaces in a generalized unit disc,” Ann. Polon. Math. 62, 193 (1995).

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of the Republic of Armenia, Yerevan, 0019, Armenia

    A. H. Karapetyan

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  1. A. H. Karapetyan
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Correspondence to A. H. Karapetyan.

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Karapetyan, A.H. On Restriction of Weighted Spaces of Holomorphic Functions in the Unit Matrix Disc to the Unit Bidisc. Lobachevskii J Math 40, 1084–1089 (2019). https://doi.org/10.1134/S1995080219080122

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  • DOI: https://doi.org/10.1134/S1995080219080122

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