Essential norm estimates for multilinear singular and fractional integrals

We derive lower two-weight estimates for the essential norm (measure of noncompactness) for multilinear Hilbert and Riesz transforms, and Riesz potential operators in Banach function lattices. As a corollary we have appropriate results in weighted Lebesgue spaces. From these statements we conclude that there is no (m + 1)-tuple of weights (v, w1, wm) for which these operators are compact from Lw1p1 ×…×Lwmpm to Lvq.

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Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).