On the optimally defined Hardy operator in 𝐿^{𝑝}-spaces

Ricker, Werner

doi:10.1090/proc/14005

On the optimally defined Hardy operator in $L^p$-spaces
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by Werner J. Ricker PDF

Proc. Amer. Math. Soc. 146 (2018), 4693-4705 Request permission

Abstract:

For each $1<p<\infty$, the optimal extension of the classical Hardy operator from $L^p (\mathbb {R}^+)$ into itself has been identified by Delgado and Soria. By relaxing the target space to be $L^p_{loc} (\mathbb {R}^+)$ we determine the optimal Hardy operator which maps into this target space.

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