Two weighted estimates of the multilinear Fractional Integral Operator between Weighted Lebesgue and Lipschitz spaces with optimal parameter

BERRA FABIO; PRADOLINI GLADIS GUADALUPE; RAMOS WILFREDO ARIEL

REVISTA DE LA UNIóN MATEMáTICA ARGENTINA

UNION MATEMATICA ARGENTINA

Lugar: Bahia Blanca; Año: 2023

0041-6932

Given an m-tuple of weights v = (v_1, . . . , v_m), we characterize the classes of pairs(w, v) involved in the boundedness properties of the multilinear fractional integral operator from the product space of Lpi (v pi ) spaces, with 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 becometrivial outside of the region obtained. We also exhibit nontrivial examples of pairs of weightsin this region.