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On an F-Algebra of Holomorphic Functions

Published online by Cambridge University Press:  20 November 2018

Hong Oh Kim
Hong Oh Kim*
Affiliation:
Korea Advanced Institute of Science and Technology, Seoul, Korea
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The complex maximal theorem of Hardy and Little-wood states:

(Mp). For 0 < p < ∞, there exists a positive constant Cp such that if f is holomorphic in the unit disc U of the complex plane then

where

The corresponding statement to the limiting case p = 0 can be stated as follows:

(M0) There exists a positive constant C0 such that if f is holomorphic in U

where log+t = max(log t, 0).

The statement (M0) is false as the following example shows.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 3 , 01 June 1988 , pp. 718 - 741
Copyright
Copyright © Canadian Mathematical Society 1988

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