Boundedness of classical operators on rearrangement-invariant spaces

We study the behaviour on rearrangement-invariant (r.i.) spaces of such classical operators of interest in harmonic analysis as the Hardy-Littlewood maximal operator (including the fractional version), the Hilbert and Stieltjes transforms, and the Riesz potential. The focus is on sharpness questions...

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Bibliographic Details
Published in:Journal of functional analysis 2020-03, Vol.278 (4), p.108341, Article 108341
Main Authors: Edmunds, David E., Mihula, Zdeněk, Musil, Vít, Pick, Luboš
Format: Article
Language:English
Subjects:
Integral operators
Optimality
Rearrangement-invariant spaces
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Summary:We study the behaviour on rearrangement-invariant (r.i.) spaces of such classical operators of interest in harmonic analysis as the Hardy-Littlewood maximal operator (including the fractional version), the Hilbert and Stieltjes transforms, and the Riesz potential. The focus is on sharpness questions, and we present characterisations of the optimal domain (or range) partner spaces when the range (domain) is fixed. When an r.i. partner space exists at all, a complete characterisation of the situation is given. We illustrate the results with a variety of examples of sharp particular results involving customary function spaces.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2019.108341