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An extension of a Hardy-Littlewood-Pólya inequality
Published online by Cambridge University Press: 20 January 2009
Extract
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.
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- Copyright © Edinburgh Mathematical Society 1978
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