Asymptotics and inversion of Riesz potentials through decomposition in radial and spherical parts
2016 (English)In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 195, no 2, 323-341 p.Article in journal (Refereed) PublishedText
It is known that radial symmetry is preserved by the Riesz potential operators and also by the hypersingular Riesz fractional derivatives typically used for inversion. In this paper, we collect properties, asymptotics, and estimates for the radial and spherical parts of Riesz potentials and for solutions to the Riesz potential equation of order one. Sharp estimates for spherical functions are provided in terms of seminorms, and a careful analysis of the radial part of a Riesz potential is carried out in elementary terms. As an application, we provide a two weight estimate for the inverse of the Riesz potential operator of order one acting on spherical functions.
Place, publisher, year, edition, pages
SPRINGER HEIDELBERG , 2016. Vol. 195, no 2, 323-341 p.
Riesz potentials; Singular integrals; Weighted spaces; Radial functions; Spherical symmetry
IdentifiersURN: urn:nbn:se:liu:diva-127414DOI: 10.1007/s10231-014-0465-8ISI: 000373086500003OAI: oai:DiVA.org:liu-127414DiVA: diva2:925584