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SOME REMARKS ON EXTREMAL PROBLEMS IN WEIGHTED BERGMAN SPACES OF ANALYTIC FUNCTIONS

  • Shamoyan, Romi F. (Bryansk University) ;
  • Arsenovic, Milos (Faculty of Mathematics University of Belgrade)
  • Received : 2011.12.01
  • Published : 2012.10.31

Abstract

We prove some sharp extremal distance results for functions in weighted Bergman spaces on the upper halfplane. We also prove new analogous results in the context of bounded strictly pseudoconvex domains with smooth boundary.

Acknowledgement

Supported by : Ministry of Education of Science, Serbia

References

  1. F. Beatrous, Jr.$L^{p}$estimates for extensions of holomorphic functions, Michigan Math. J. 32 (1985), no. 3, 361-380. https://doi.org/10.1307/mmj/1029003244
  2. D. Bekolle, C. Berger, L. Coburn, and K. Zhu, BMO in the Bergman metric on bounded symmetric domains, J. Funct. Anal. 93 (1990), no. 2, 310-350. https://doi.org/10.1016/0022-1236(90)90131-4
  3. D. Bekolle and A. Bonami, Estimates for the Bergman and Szego projections in two symmetric domains, Colloq. Math. 68 (1995), no. 1, 81-100. https://doi.org/10.4064/cm-68-1-81-100
  4. D. Bekolle, A. Bonami, G. Garrigos, C. Nana, M. Peloso, and F. Ricci Lecture notes on Bergman projections on tube domains over cones: an analytic and geometric viewpoint, preprint 2002.
  5. M. Djrbashian and A. Djrbashian, Integral representations for some classes of analytic functions in the half-plane, Dokl Acad NAuk 285 (1985), 547-550.
  6. A. Djrbashian and K. Karapetyan, Integral inequalities between conjugate pluriharmonic functions in multidimensional domains, Izv NAts Akad Nauk Armenii (1988), 216-236.
  7. M. Djrbashian and F. Shamoian, Topics in the theory of $A_{p}^{\alpha}$ classes, Teubner Texte zur Mathematik, 1988, v 105.
  8. P. Duren, Theory of $H^{p}$ Spaces, Academic Press, 1970.
  9. J. Faraut and A. Koranyi, Function spaces and reproducing kernels on bounded symmetric domains, J. Funct. Anal. 88 (1990), no. 1, 64-89. https://doi.org/10.1016/0022-1236(90)90119-6
  10. R. Shamoyan and O. Mihic, On new estimates for distances in analytic function spaces in higher dimension, Sib. Elektron. Mat. Izv. 6 (2009), 514-517.
  11. R. Shamoyan and O. Mihic, On new estimates for distances in analytic function spaces in the unit disk, polydisk and unit ball, to appear in Bol. Asoc. MAt. Venez.

Cited by

  1. ON DISTANCE ESTIMATES AND ATOMIC DECOMPOSITIONS IN SPACES OF ANALYTIC FUNCTIONS ON STRICTLY PSEUDOCONVEX DOMAINS vol.52, pp.1, 2015, https://doi.org/10.4134/BKMS.2015.52.1.085