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2013 | 11 | 6 | 985-1003
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Bloch-to-Hardy composition operators

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let φ be a holomorphic mapping between complex unit balls. We characterize those regular φ for which the composition operators C φ: f ↦ f ○ φ map the Bloch space into the Hardy space.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
6
Strony
985-1003
Opis fizyczny
Daty
wydano
2013-06-01
online
2013-03-28
Twórcy
  • St. Petersburg Department of V.A. Steklov Mathematical Institute, Fontanka 27, St. Petersburg, 191023, Russia, dubtsov@pdmi.ras.ru
  • Department of Mathematics, St. Petersburg State University of Architecture and Civil Engineering, 2nd Krasnoarmeiskaya Str. 4, St. Petersburg, 190005, Russia, petrovap6139@mail.ru
Bibliografia
  • [1] Ahern P., Bruna J., Maximal and area integral characterizations of Hardy-Sobolev spaces in the unit ball of ℂn, Rev. Mat. Iberoamericana, 1988, 4(1), 123–153 http://dx.doi.org/10.4171/RMI/66[Crossref]
  • [2] Ahern P., Rudin W., Bloch functions, BMO, and boundary zeros, Indiana Univ. Math. J., 1987, 36(1), 131–148 http://dx.doi.org/10.1512/iumj.1987.36.36007[Crossref]
  • [3] Beatrous F., Burbea J., Holomorphic Sobolev Spaces on the Ball, Dissertationes Math. (Rozprawy Mat.), 276, Polish Academy of Sciencies, Warsaw, 1989
  • [4] Blasco O., Lindström M., Taskinen J., Bloch-to-BMOA compositions in several complex variables, Complex Var. Theory Appl., 2005, 50(14), 1061–1080
  • [5] Doubtsov E., Growth spaces on circular domains: composition operators and Carleson measures, C. R. Math. Acad. Sci. Paris, 2009, 347(11–12), 609–612 http://dx.doi.org/10.1016/j.crma.2009.04.003[Crossref]
  • [6] Doubtsov E., Hyperbolic BMOA classes, J. Math. Anal. Appl., 2012, 391(1), 57–66 http://dx.doi.org/10.1016/j.jmaa.2012.02.032[Crossref]
  • [7] Doubtsov E., Bloch-to-BMOA compositions on complex balls, Proc. Amer. Math. Soc., 2012, 140(12), 4217–4225 http://dx.doi.org/10.1090/S0002-9939-2012-11280-8[WoS][Crossref]
  • [8] Kwon E.G., Composition of Blochs with bounded analytic functions, Proc. Amer. Math. Soc., 1996, 124(5), 1473–1480 http://dx.doi.org/10.1090/S0002-9939-96-03191-7[Crossref]
  • [9] Kwon E.G., Hyperbolic mean growth of bounded holomorphic functions in the ball, Trans. Amer. Math. Soc., 2003, 355(3), 1269–1294 http://dx.doi.org/10.1090/S0002-9947-02-03169-0[Crossref]
  • [10] Kwon E.G., Hyperbolic g-function and Bloch pullback operators, J. Math. Anal. Appl., 2005, 309(2), 626–637 http://dx.doi.org/10.1016/j.jmaa.2004.10.042[Crossref]
  • [11] Kwon E.G., Bloch-Bergman pullbacks with logarithmic weights, Integral Equations Operator Theory, 2009, 64(2), 251–260 http://dx.doi.org/10.1007/s00020-009-1690-1[Crossref]
  • [12] Ramey W., Ullrich D., Bounded mean oscillation of Bloch pull-backs, Math. Ann., 1991, 291(4), 591–606 http://dx.doi.org/10.1007/BF01445229[Crossref]
  • [13] Shi J., Luo L., Composition operators on the Bloch space of several complex variables, Acta Math. Sin. (Engl. Ser.), 2000, 16(1), 85–98 http://dx.doi.org/10.1007/s101149900028[Crossref]
  • [14] Stein E.M., Singular Integrals and Differentiability Properties of Functions, Princeton Math. Ser., 30, Princeton University Press, Princeton, 1970
  • [15] Yamashita S., Hyperbolic Hardy class H 1, Math. Scand., 1979, 45(2), 261–266
  • [16] Zhu K., Spaces of Holomorphic Functions in the Unit Ball, Grad. Texts in Math., 226, Springer, New York, 2005
  • [17] Zygmund A., Trigonometric Series, I, II, 2nd ed., Cambridge University Press, New York, 1959
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0229-5
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