Two-weighted estimates of the multilinear fractional integral operator between weighted Lebesgue and Lipschitz spaces with optimal parameters

Fabio Berra ^[1] ; Gladis Pradolini ^[1] ; Wilfredo Ramos ^[1]
1. [1] CONICET, Argentina
Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 66, Nº. 1, 2023, págs. 69-90
Idioma: inglés
DOI: 10.33044/revuma.4346
Enlaces
- Texto completo (pdf)
Resumen
- Given an m-tuple of weights ~v = (v1, . . . , vm), we characterize the classes of pairs (w, ~v) involved in the boundedness properties of the multilinear fractional integral operator from Qmi=1 Lpi vpii into suitable Lipschitz spaces associated to a parameter δ, Lw(δ). Our results generalize some previous estimates not only for the linear case but also for the unweighted problem in the multilinear context. We emphasize the study related to the range of the parameters involved in the problem described above, which is optimal in the sense that they become trivial outside of the region obtained. We also exhibit nontrivial examples of pairs of weights in this region