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On the optimally defined Hardy operator in $ L^p$-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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Werner J. Ricker
Affiliation: Math.-Geogr. Fakultät, Katholische Universität Eichstätt-Ingolstadt, D-85072 Eichstätt, Germany
Email: werner.ricker@ku.de

DOI: https://doi.org/10.1090/proc/14005
Keywords: Hardy operator, $L^p_{loc}$-space, optimal domain, vector measure, integral representation.
Received by editor(s): July 28, 2017
Received by editor(s) in revised form: October 30, 2017
Published electronically: August 10, 2018
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2018 American Mathematical Society