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An extension of a Hardy-Littlewood-Pólya inequality

Published online by Cambridge University Press:  20 January 2009

A. Erdélyi
A. Erdélyi
Affiliation:
Department of Mathematics, University of Edinburgh.
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The Hardy-Littlewood-Pólya inequality in question can be written in the form

Here and throughout, all functions are assumed to be locally integrable on ]0,∞[, 1≤p≤∞,p-1+(p′)-1=1 (with similar conventions for q,r,s), is the usual norm on Lp(0,∞), and if the right hand side is finite, then (1.1) is understood to mean that

defines a locally integrable function Kf for which (1.1) holds.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 21 , Issue 1 , March 1978 , pp. 11 - 15
Copyright
Copyright © Edinburgh Mathematical Society 1978

References

REFERENCES

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