A new Proof of Hardys Identity

Shatha S.Alhily

Abstract


We present a full proof of Hardys identity which is of course well known of all the people interested in this field. Seemingly, there is no convenient reference, at least to our knowledge. This is what prompted us to try the proof it.


Keywords


Cauchy-Riemann equations ( polar coordinates); Estimation the Integral means ; Univalent function.

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References


Ch. Pommerenke. On the integral means of the derivative of a univalent function. J. London . Math.Soc, 32(2):254258, 1985.

Ch. Pommerenke. Univalent functions. Vandenhoeck and Ruprecht, Ga ?ttingen, Germany, 1975.

J. E. Littlewood, Lectures on the theory of functions , Oxford University Press, 1944.

W. K. Hayman, Multivalent functions , Cambridge University Press, 1958.


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