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Some further results concerning the integrals of moduli of regular functions along curves of certain types

Published online by Cambridge University Press:  24 October 2008

R. M. Garriel
R. M. Garriel
Affiliation:
Queens' College.
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Extract

In a paper* of some time back I gave the following theorem:

If f(z) is a regular function of z for z inside and on a circle Τ, and C is any convex curve inside Τ, and λ>0, then

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 25 , Issue 2 , April 1929 , pp. 139 - 144
Copyright
Copyright © Cambridge Philosophical Society 1929

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References

* “Some results concerning the integrals of moduli of regular functions along curves of certain types”, Proceedings of the London Mathematical Society, Vol. 28, pp. 121–127 (1926).Google Scholar

* See the case for the circle, discussed fully by Riesz, F. and Fejér, L.: “Über einige funktionentheoretische Ungleichungen”, Math. Zeitschrift, 2 (1921), 305–314.Google Scholar