Boundedness of multilinear commutators of generalized fractional integrals

Abstract Let L be the infinitesimal generator of an analytic semigroup on L2(ℝn ) with Gaussian kernel bound, and let L–α /2 be the fractional integral of L for 0 < α < n. Suppose that b = (b1, b2, …, bm ) is a finite family of locally integral functions, then the multilinear commutator generated by b and L–α /2 is defined by L–α /2bf = [bm , …, [b2, [b1, L–α /2]], …, ] f, where m ∈ ℤ+. When b1, b2, …, bm ∈ BMO or bj ∈ Λ (0 < βj < 1) for 1 ≤ j ≤ m, the authors study the boundedness of L–α /2b. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)