Optimal domain for the Hardy operator

2006/02/20 by O. Delgado, Olvido Delgado, Javier Soria +2
Mathematics · #46B25 #46E30 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.CA #math.FA #msc:46B25 #msc:46E30

paper · pdf · doi:10.48550/arxiv.math/0602426

15 pages

arxiv created 2006/02/20 · openalex publication_date 2006/02/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the optimal domain for the Hardy operator considered with values in a rearrangement invariant space. In particular, this domain can be represented as the space of integrable functions with respect to a vector measure defined on a δ-ring. A precise description is given for the case of the minimal Lorentz spaces.

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