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A Generalization Of An Inequality Of Hardy and Littlewood

Published online by Cambridge University Press:  20 November 2018

K. T. Smith
K. T. Smith*
Affiliation:
University of Kansas
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1. Introduction. A well-known inequality of Hardy-Littlewood reads as follows (4): if p > 1 and f > 0, then

,

where is defined as the supremum of the numbers

the constant depends on p only. The statement obtained by putting p = 1 is false; its substitute reads:

the constants depend on p but not on f.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 157 - 170
Copyright
Copyright © Canadian Mathematical Society 1956

References

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