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abstract: '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.'
address:
- 'David E. Edmunds, Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9QH, UK'
- 'Zdeněk Mihula, Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic'
- 'Vít Musil, Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic'
- 'Luboš Pick, Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic'
author:
- 'David E. Edmunds, Zdeněk Mihula, Vít Musil and Luboš Pick'
bibliography:
- 'classical-operators-arxiv.bib'
date: '31/10/2019'
title: 'Boundedness of classical operators on rearrangement-invariant 