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Properties of the Coefficients of Orthonormal Sequences

Published online by Cambridge University Press:  20 November 2018

P. S. Bullen
P. S. Bullen*
Affiliation:
University of British Columbia
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In this paper we consider complete orthonormal sequences defined on the interval [0, 1] and satisfying an inequality of the type

(1)

for all n and some sequence {Fn}. Such sequences were first considered by Zygmund and Marcinkiewicz (8). They extended the well-known results of Hausdorff-Young and Paley, originally proved for the case v = ∞, Fn = M for all n (12). We will consider cases of equality in t he Hausdorff-Young theorems and certain limiting cases of the Paley theorems. Application of these results and the results in (8) will be made to functions harmonic in the unit α-sphere.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 305 - 315
Copyright
Copyright © Canadian Mathematical Society 1961

References

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