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Image Area and the Weighted Subspaces of Hardy Spaces

Published online by Cambridge University Press:  20 November 2018

E. G. Kwon*
Affiliation:
Department of Mathematics Education, Andong National University, Andong 760-749, (South) Korea
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Abstract

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Let Hp,ϕ be the subspace of Hardy space Hp consisting of those f ∊ Hp(Bn) satisfying where ϕ is a positive decreasing differentiable function on [0, 1) with ϕ(1—) = 0. Concerning image area growth, criteria for f to be of Hp,ϕ are considered extending known results for Hp.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Ahern, P. R., The mean modulus and derivatives of an inner function, Indianna University Math. J., 28 No. 2(1979), 311347.Google Scholar
2. Duren, P. L., Theory of Hp spaces, Academic Press, New York, NY 1970.Google Scholar
3. Holland, F. and Twomey, J. B., On Hardy classes and the area function, J. London Math. Soc, (2) 17 (1978), 275283.Google Scholar
4. Kim, H. O., Derivatives of Blaschke products, Pacific J. Math., 114 (1984), 175191.Google Scholar
5. Kim, H. O., Kim, S. M. and Kwon, E. G., A note on the space Hp'a , Communications of the Korean Math. Soc, Vol. 2 No. 1 (1981), 4751.Google Scholar
6. Piranian, G. and Rudin, W., Lusin's theorem on areas of conformai maps, Michigan Math. J., 3 (1955-1956), 191199.Google Scholar
7. Rudin, W., Function theory in the unit ball of Cn , Springer Verlag, New York, 1980.Google Scholar
8. Yamashita, S., Criteria for functions to be Hardy class Hp , Proceedings of A.M.S., Vol. 75 No. 1 (1979), 6972.Google Scholar
9. Yamashita, S., Holomorphic functions and area integrals, Bollettino U.M.I. (6) 1-A (1982), 115-120.Google Scholar