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==Proofs==
===Case ''p'' = 2===
To prove the result for ''H''<sup>2</sup> it suffices to show that for ''f'' a polynomial<ref>{{harvnb|Nikolski|2002|
:<math>\displaystyle{\|C_h f\|^2 \le \|f\|^2,}</math>
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*{{citation|last=Duren|first= P. L.|title=Theory of H <sup>p</sup> spaces|series=Pure and Applied Mathematics|volume= 38|
publisher= Academic Press|year=1970}}
*{{citation|last=Littlewood|first=J. E.|title=On inequalities in the theory of functions|journal=Proc. London Math. Soc.|year=1925|volume=23|pages=
*{{citation|last=Nikolski|first=N. K.|title=Operators, functions, and systems: an easy reading. Vol. 1. Hardy, Hankel, and Toeplitz|series= Mathematical Surveys and Monographs|volume= 92|publisher= American Mathematical Society|year= 2002|id= ISBN 0-8218-1083-9}}
*{{citation|first=F.|last=Riesz|title=Sur une inégalite de M. Littlewood dans la théorie des fonctions|journal= Proc. London Math. Soc.|volume= 23|year=1925|pages=
*{{citation|last=Shapiro|first=J. H.|title=Composition operators and classical function theory|series=Universitext: Tracts in Mathematics|publisher= Springer-Verlag|year= 1993|id=ISBN 0-387-94067-7}}
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