Equivalent characterizations of Bloch functions

Zhangjian Hu

Colloquium Mathematicae (1994)

  • Volume: 67, Issue: 1, page 99-108
  • ISSN: 0010-1354

Abstract

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In this paper we obtain some equivalent characterizations of Bloch functions on general bounded strongly pseudoconvex domains with smooth boundary, which extends the known results in [1, 9, 10].

How to cite

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Hu, Zhangjian. "Equivalent characterizations of Bloch functions." Colloquium Mathematicae 67.1 (1994): 99-108. <http://eudml.org/doc/210267>.

@article{Hu1994,
abstract = {In this paper we obtain some equivalent characterizations of Bloch functions on general bounded strongly pseudoconvex domains with smooth boundary, which extends the known results in [1, 9, 10].},
author = {Hu, Zhangjian},
journal = {Colloquium Mathematicae},
keywords = {bounded strongly pseudoconvex domain; holomorphic functions; Bloch space},
language = {eng},
number = {1},
pages = {99-108},
title = {Equivalent characterizations of Bloch functions},
url = {http://eudml.org/doc/210267},
volume = {67},
year = {1994},
}

TY - JOUR
AU - Hu, Zhangjian
TI - Equivalent characterizations of Bloch functions
JO - Colloquium Mathematicae
PY - 1994
VL - 67
IS - 1
SP - 99
EP - 108
AB - In this paper we obtain some equivalent characterizations of Bloch functions on general bounded strongly pseudoconvex domains with smooth boundary, which extends the known results in [1, 9, 10].
LA - eng
KW - bounded strongly pseudoconvex domain; holomorphic functions; Bloch space
UR - http://eudml.org/doc/210267
ER -

References

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  1. [1] S. Axler, The Bergman space, the Bloch space and commutators of multiplication operators, Duke Math. J. 53 (1986), 315-332. Zbl0633.47014
  2. [2] C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1-65. Zbl0289.32012
  3. [3] S. G. Krantz, Function Theory of Several Complex Variables, Wiley, New York, 1982. Zbl0471.32008
  4. [4] S. G. Krantz and D. Ma, The Bloch functions on strongly pseudoconvex domains, Indiana Univ. Math. J. 37 (1988), 145-165. Zbl0628.32006
  5. [5] H. Li, BMO, VMO and Hankel operators on the Bergman space of strongly pseudoconvex domains, J. Funct. Anal. 106 (1992), 375-408. 
  6. [6] H. Li, Hankel operators on the Bergman space of strongly pseudoconvex domains, preprint. Zbl0817.47037
  7. [7] W. Rudin, Function Theory in the Unit Ball of ℂ n , Springer, New York, 1980. 
  8. [8] E. M. Stein, Boundary Behavior of Holomorphic Functions of Several Complex Variables, Princeton University Press, Princeton, N.J., 1972. Zbl0242.32005
  9. [9] K. Stroethoff, Besov-type characterisations for the Bloch space, Bull. Austral. Math. Soc. 39 (1989), 405-420. Zbl0661.30040
  10. [10] J. Zhang, Some characterizations of Bloch functions on strongly pseudoconvex domains, Colloq. Math. 63 (1992), 219-232. Zbl0761.32005

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