Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-06-17T18:11:42.163Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Duren, P. L., Theory of HP spaces (Academic Press, New York, NY, 1970).Google Scholar
[2]Jawerth, B. and Torchinsky, A., “On a Hardy and Littlewood imbedding theorem”. Preprint.Google Scholar
[3]Kim, H. O., “Derivatives of Blaschke products”, Pacific J. Math., 114 (1984), 175–190.CrossRefGoogle Scholar
[4]Littlewood, J. E., Lectures on the theory of functions (Clarenden Press, Oxford, 1944).Google Scholar