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SCHWARZ LEMMA FOR HOLOMORPHIC MAPPINGS IN THE UNIT BALL

  • DAVID KALAJ (a1)

Abstract

In this note, we establish a Schwarz–Pick type inequality for holomorphic mappings between unit balls B n and B m in corresponding complex spaces. We also prove a Schwarz-Pick type inequality for pluri-harmonic functions.

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References

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1. Chen, Sh. and Rasila, A., Schwarz-Pick type estimates of pluriharmonic mappings in the unit polydisk, Illinois J. Math. 58 (4) (2014), 10151024.
2. Kalaj, D. and Markovic, M., Norm of the Bergman projection, Math. Scand. 115 (1) (2014), 143160.
3. Kalaj, D. and Vuorinen, M., On harmonic functions and the Schwarz lemma, Proc. Am. Math. Soc. 140 (1) (2012), 161165.
4. Pavlović, M., A Schwarz lemma for the modulus of a vector-valued analytic function, Proc. Amer. Math. Soc. 139 (3) (2011), 969973.
5. Perälä, A., Bloch space and the norm of the Bergman projection, Ann. Acad. Sci. Fenn., Math. 38 (2) (2013), 849853.
6. Rudin, W., Function theory of the unit ball in C n (Springer, New York, 1980).
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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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