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Boundary properties of analytic and harmonic functions with values in Banach space

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Literature cited

  1. A. V. Bukhvalov, “Hardy spaces of vector-valued functions,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,65, 5–16 (1976).

    Google Scholar 

  2. A. A. Danilevich, “Some boundary properties of abstract analytic functions, and their applications,” Mat. Sb.,100, No. 4, 507–533 (1976).

    Google Scholar 

  3. R. Ryan, “Boundary values of analytic vector valued functions,” Proc. Koninkl. Nederl. Acad.,A65, No. 5, 558–572 (1962).

    Google Scholar 

  4. A. A. Danilevich, “The theory of bounded analytic functions,” Sb. Mat. Anal. Teor. Funktsii,3, Izd. Mosk. Obl. Pedagog. Inst., 1–211 (1974).

  5. C. Grossetete, “Sur certaines classes de fonctions harmoniques dans le disque a valeur dans un espace vectoriel topologique localement convexe,” C.R. Acad. Sci. Paris,A273, No. 22, A1048-A1051 (1971).

    Google Scholar 

  6. L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  7. A. V. Bukhvalov, “Spaces with mixed norm,” Vestn. Leningr. Gos. Univ., No. 19, 5–12 (1973).

    Google Scholar 

  8. S. D. Chatterji, “Martingale convergence and the Radon-Nikodim theorem in Banach spaces,” Math. Scand.,22, 21–41 (1968).

    Google Scholar 

  9. S. Bochner and A. E. Taylor, “Linear functionals on certain spaces of abstractly valued functions,” Ann. Math. (2),39, 913–944 (1938).

    Google Scholar 

  10. A. V. Bukhvalov, “The analytic representation of linear operators using measurable vector-functions,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 7, 21–31 (1977).

    Google Scholar 

  11. A. Zygmund, Trigonometrical Series, Vol. 2, Cambridge Univ. Press.

  12. A. Pelezynski, “Banach spaces of analytic functions and absolutely summing operators,” CBMS Reg. Conf. Ser. in Math.,30, 91 (1977).

    Google Scholar 

  13. V. P. Khavin, “The spaces H∞ and L1/H 10 ,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,39, 120–148 (1974).

    Google Scholar 

  14. T. Figiel, W. B. Johnson, and L. Tzafriri, “On Banach lattices and spaces, having local unconditional structure, with applications to Lorentz function spaces,” J. Appr. Theory,13, No. 4, 395–412 (1975).

    Google Scholar 

  15. W. B. Johnson and L. Tzafriri, “Some more Banach spaces which do not have local unconditional structure,” Houston J. Math.,3, No. 1, 55–60 (1977).

    Google Scholar 

  16. K. Huffman, Banach Spaces of Analytic Functions, Prentice-Hall (1962).

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Authors and Affiliations

  1. Scientific-Research Institute for Automated Management Systems, USSR

    A. V. Bukhvalov & A. A. Danilevich

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  1. A. V. Bukhvalov
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  2. A. A. Danilevich
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Translated from Matematicheskie Zametki, Vol. 31, No. 2, pp. 203–214, February, 1982.

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Bukhvalov, A.V., Danilevich, A.A. Boundary properties of analytic and harmonic functions with values in Banach space. Mathematical Notes of the Academy of Sciences of the USSR 31, 104–110 (1982). https://doi.org/10.1007/BF01158129

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