Proof of a theorem of Paley
Published online by Cambridge University Press: 24 October 2008
Extract
1. Let f(x) be a real function of period 2π, integrable L over (0, 2π), and let
By sn(x) and σn (x) we denote respectively the partial sums and the first arithmetic means of the series (1·1). Similarly, by and we denote the partial sums and the first arithmetic means of the series
conjugate to (1·1). By we mean the function conjugate to f(x), that is
where the integral is taken in the principal-value sense.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 34 , Issue 2 , April 1938 , pp. 125 - 133
- Copyright
- Copyright © Cambridge Philosophical Society 1938
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