2019/03/31 by D. E. Edmunds, David E. Edmunds, Zdeněk Mihula +2
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Hardy space #Hilbert space #Invariant (physics) #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Operator (biology) #Pure mathematics #math.FA #msc:26D20 #msc:46B70 #msc:46E30 #msc:47B38
paper · pdf · doi:10.1016/j.jfa.2019.108341
published as J. Funct. Anal., 278(4):108341, 2020 · 38 pages
openalex publication_date 2019/10/10 · arxiv created 2019/10/31 · arxiv updated 2020/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the behaviour on rearrangement-invariant 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 a rearrangement-invariant 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.