Estimates for Multilinear Commutators of Generalized Fractional Integral Operators on Weighted Morrey Spaces

Abstract EN

Let L be the infinitesimal generator of an analytic semigroup on L 2 ( R n ) with Gaussian kernel bounds, and let L - α / 2 be the fractional integrals of L for 0 < α < n .

Assume that b → = ( b 1 , b 2 , … , b m ) is a finite family of locally integrable functions; then the multilinear commutators generated by b → and L - α / 2 are defined by L b → - α / 2 f = [ b m , … , [ b 2 , [ b 1 , L - α / 2 ] ] , … ] f .

Assume that b j belongs to weighted BMO space, j = 1,2 , … , m ; the authors obtain the boundedness of L b → - α / 2 on weighted Morrey spaces.

As a special case, when L = - Δ is the Laplacian operator, the authors also obtain the boundedness of the multilinear fractional commutator I α b → on weighted Morrey spaces.

The main results in this paper are substantial improvements and extensions of some known results.