Regularity for commutators of the local multilinear fractional maximal operators

Abstract

In this paper we introduce and study the commutators of the local multilinear fractional maximal operators and a vector-valued function b⃗ = (b1, …, bm). Under the condition that each bi belongs to the first order Sobolev spaces, the bounds for the above commutators are established on the first order Sobolev spaces.

Keywords

• commutator
• local multilinear fractional maximal operator
• sobolev space
• 42b25
• 46e35