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

Ricker, Werner

doi:10.1090/proc/14005

On the optimally defined Hardy operator in -spaces

Author: Werner J. Ricker
Journal: Proc. Amer. Math. Soc. 146 (2018), 4693-4705
MSC (2010): Primary 46E30, 47A67; Secondary 46G10, 47B38
DOI: https://doi.org/10.1090/proc/14005
Published electronically: August 10, 2018
MathSciNet review: 3856138
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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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