Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ESSENTIAL NORM OF THE COMPOSITION OPERATORS BETWEEN BERGMAN SPACES OF LOGARITHMIC WEIGHTS

  • Kwon, Ern Gun (Department of Mathematics Education Andong National University) ;
  • Lee, Jinkee (Department of Mathematics Pusan National University)
  • Received : 2016.01.09
  • Published : 2017.01.31
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Abstract

We obtain some necessary and sufficient conditions for the boundedness of the composition operators between weighted Bergman spaces of logarithmic weights. In terms of the conditions for the boundedness, we compute the essential norm of the composition operators.

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References

  1. C. C. Cowen and B. D. Maccluer, Composition Operators on Spaces of Analytic Functions, CRC Press, 1995.
  2. E. G. Kwon and J. Lee, Composition operators between Bergman Spaces of logarithmic weights, Internat. J. Math. 26 (2015), no. 9, 1550068, 14 pp. https://doi.org/10.1142/S0129167X15500688
  3. J. A. Pelaez and J. Rattya, Trace class criteria for Toeplitz and composition operators on small Bergman spaces, preprint (submitted), http://arxiv.org/abs/1501.00131.
  4. F. Perez-Gonzalez, J. Rattya, and D. Vukotic, On composition operators acting between Hardy and weighted Beregman spaces, Expo. Math. 25 (2007), no. 4, 309-323. https://doi.org/10.1016/j.exmath.2007.03.001
  5. J. H. Shapiro, The essential norm of a composition operator, Ann. Math. 127 (1987), no. 2, 375-404.
  6. W. Smith, Composition operators between Bergman and Hardy spaces, Trans. Amer. Math. Soc. 348 (1996), no. 6, 2331-2348. https://doi.org/10.1090/S0002-9947-96-01647-9