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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Growth of harmonic conjugates in the unit disc

Author: Miroljub Jevtić
Journal: Proc. Amer. Math. Soc. 98 (1986), 41-45
MSC: Primary 31A05; Secondary 30C99
MathSciNet review: 848872
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Abstract: Assuming some mild regularity conditions on a positive nondecreasing function $ \psi (x) = O({x^a})$ (for some $ a > 0,x \to \infty $), we show that

$\displaystyle {M_p}(r,u) = O\left( {\psi \left( {\frac{1} {{1 - r}}} \right)} \right)(r \to 1,0 < p < 1)$

implies $ {M_p}(r,v) = O{({\tilde \psi ^p}(1/(1 - r)))^{1/p}}$, where $ u(z) + iv(z)$ is holomorphic in the open unit disc and

$\displaystyle {\tilde \psi ^p}(x) = \int_{1/2}^x {\frac{{{\psi ^p}(t)}}{t}dt,\quad x \geqslant \frac{1}{2}.} $

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Additional Information

PII: S 0002-9939(1986)0848872-3
Keywords: Conjugate functions
Article copyright: © Copyright 1986 American Mathematical Society

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