Geodesic
Some Extensions of the Hausdorff-Young and Paley Theorems
Canadian mathematical bulletin, Tome 4 (1961) no. 2, pp. 123-138

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Orthonormal sequences, o.n. s., {φn} defined on [0,1] and satisfying 1 have been studied in [3] and [1]. One of the objects of this paper is to indicate that the methods used to study such o. n. s. can be used for a much wider class, and that, although there seems to be no super theorem to cover all cases, a knowledge of the results and methods of proof in some fairly broad special cases enables one to state and prove theorems for other classes of o. n. s. 
Bullen, P. S. Some Extensions of the Hausdorff-Young and Paley Theorems. Canadian mathematical bulletin, Tome 4 (1961) no. 2, pp. 123-138. doi: 10.4153/CMB-1961-014-8
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     author = {Bullen, P. S.},
     title = {Some {Extensions} of the {Hausdorff-Young} and {Paley} {Theorems}},
     journal = {Canadian mathematical bulletin},
     pages = {123--138},
     year = {1961},
     volume = {4},
     number = {2},
     doi = {10.4153/CMB-1961-014-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1961-014-8/}
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