Abstract
We proved ifk(z)∈H q (q≥1),g(z) is analytic on |z|=1,\(\left\| {g(e^{i\theta } ) + k(e^{i\theta } )} \right\|q = \mathop {\min }\limits_{h \in H^q } \left\| {g(e^{i\theta } ) + h(e^{i\theta } )} \right\|\), thenk′(z)∈H 1, especially, ifq=1, thenk(z) is an analytic function on the closed unit disk |z|≤1.
Similar content being viewed by others
References
Yusuf Abu-Muhanna. Support points of the unit ball ofH p(1≤p≤∞).Proc Am Math Soc, 1983,89(10): 229–235
D J Hallenbeck, T H MacGregor.Linear problems and convexity techniques in geometric function theory. New York: Pitman Advanced Publishing Program, 1985, 42
P L Duren.Theory of H p spaces. New York: Academic Press, 1970, 130, 42
Author information
Authors and Affiliations
Additional information
Peng Zhigang: born in June 1970, Ph. D
Rights and permissions
About this article
Cite this article
Zhigang, P. A sufficient condition fork′(z)(k(z)∈H q,q≥1) to be ofH 1 . Wuhan Univ. J. Nat. Sci. 2, 139–141 (1997). https://doi.org/10.1007/BF02827815
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02827815