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A note on a space Hp, a of holomorphic functions

Published online by Cambridge University Press:  17 April 2009

H. O. Kim ,
S. M. Kim  and
E. G. Kwon
H. O. Kim
Affiliation:
Department of Applied Mathematics, Korea Advanced Institute of Science and Technology, P.O. Box 150, Cheongryang, Seoul, Korea
S. M. Kim
Affiliation:
Department of Mathematics, Andong University, Andong 660., Korea
E. G. Kwon
Affiliation:
Department of Mathematics, Seoul National University, Seoul, 151, Korea
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Abstract

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For 0 < p < ∞ and 0 ≤a; ≤ 1, we define a space Hp, a of holomorphic functions on the unit disc of the complex plane, for which Hp, 0 = H∞, the space of all bounded holomorphic functions, and Hp, 1 = Hp, the usual Hardy space. We introduce a weak type operator whose boundedness extends the well-known Hardy-Littlewood embedding theorem to Hp, a, give some results on the Taylor coefficients of the functions of Hp, a and show by an example that the inner factor cannot be divisible in Hp, a.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 35 , Issue 3 , June 1987 , pp. 471 - 479
Copyright
Copyright © Australian Mathematical Society 1987

References

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