# Equivalent characterizations of Bloch functions

Colloquium Mathematicae (1994)

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

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topHu, 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

top- [1] S. Axler, The Bergman space, the Bloch space and commutators of multiplication operators, Duke Math. J. 53 (1986), 315-332. Zbl0633.47014
- [2] C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1-65. Zbl0289.32012
- [3] S. G. Krantz, Function Theory of Several Complex Variables, Wiley, New York, 1982. Zbl0471.32008
- [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] H. Li, BMO, VMO and Hankel operators on the Bergman space of strongly pseudoconvex domains, J. Funct. Anal. 106 (1992), 375-408.
- [6] H. Li, Hankel operators on the Bergman space of strongly pseudoconvex domains, preprint. Zbl0817.47037
- [7] W. Rudin, Function Theory in the Unit Ball of ${\u2102}^{n}$, Springer, New York, 1980.
- [8] E. M. Stein, Boundary Behavior of Holomorphic Functions of Several Complex Variables, Princeton University Press, Princeton, N.J., 1972. Zbl0242.32005
- [9] K. Stroethoff, Besov-type characterisations for the Bloch space, Bull. Austral. Math. Soc. 39 (1989), 405-420. Zbl0661.30040
- [10] J. Zhang, Some characterizations of Bloch functions on strongly pseudoconvex domains, Colloq. Math. 63 (1992), 219-232. Zbl0761.32005

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