Boundedness of multilinear commutators of generalized fractional integrals

Abstract

Let L be the infinitesimal generator of an analytic semigroup on L 2 (R n ) 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 bywhere m ∈ Z + . When b1, b2, . . . , bm ∈ BMO or bj ∈Λ β j (0 < βj < 1) for 1 ≤ j ≤ m, the authors study the boundedness of L −α/2 b .

Some Estimates for Commutators of Fractional Integrals Associated to Operators with Gaussian Kernel Bounds on Weighted Morrey Spaces

“…Thus, by using the Gaussian upper bound (1.1) and the expression (3.2), we can deduce (see [7] and [15])…”

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

“…Simultaneously, the theory on multilinear integral operators and multilinear commutators has attracted much attention as a rapid developing field in harmonic analysis. Mo and Lu [3] studied the ( , ) boundedness of the multilinear commutators − /2 ⃗ , where ⃗ = ( 1 , . .…”

“…Motivated by [1,3,5,6], it is natural to raise the following question: how to establish corresponding boundedness of the multilinear commutator − /2 ⃗ on the weighted Morrey space, where ⃗ = ( 1 , . .…”

“…The question is not motivated only by a mere quest to extend the multilinear commutator − /2 ⃗ from the classical commutator [ , ] but rather by their natural appearance in analysis (see [3]).…”

The Boundedness of Toeplitz-Type Operators on Vanishing-Morrey Spaces

“…Lemma 2.1 [5] . For 0 < α < n, let L −α/2 and I α be defined as above, then there exists a constant C > 0 such that…”