Estimates for Multilinear Commutators of Generalized Fractional Integral Operators on Weighted Morrey Spaces. (6th April 2015) - He, Sha; Zheng, Taotao; Tao, Xiangxing
Abstract : LetL be the infinitesimal generator of an analytic semigroup onL 2 ( R n ) with Gaussian kernel bounds, and letL - α / 2 be the fractional integrals ofL for0 < α < n . Assume thatb → = ( b 1, b 2, …, b m ) is a finite family of locally integrable functions; then the multilinear commutators generated byb → andL - α / 2 are defined byL b → - α / 2 f = [ b m, …, [ b 2, [ b 1, L - α / 2 ] ], … ] f . Assume thatb j belongs to weighted BMO space, j = 1, 2, …, m ; the authors obtain the boundedness ofL b → - α / 2 on weighted Morrey spaces. As a special case, whenL = - Δ is the Laplacian operator, the authors also obtain the boundedness of the multilinear fractional commutatorI α b → on weighted Morrey spaces. The main results in this paper are substantial improvements and extensions of some known results.