Weighted inequalities for the Riesz potential on the sphere. Issue 6 (2nd June 2016)

• Record Type: Journal Article
• Authors: Arenas, A.; Ciaurri, Ó.; Labarga, E.
• Is Part Of: Integral transforms and special functions. Volume 27:Issue 6(2016)
• Page Start: 511
• Page End: 522
• Publication Date: 2016-06-02
• Subjects: Riesz potential -- conformal Laplacian -- weighted inequalities -- ultraspherical polynomials; 42B20; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2016.1158176
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: We prove a version of the Stein–Weiss inequality for the Riesz potential of the conformal Laplacian on the sphere. Moreover, we show that the result can be improved for functions invariant under the action of the group S O ( d − 1 ) . This last result will be a consequence of a more general one for ultraspherical expansions.