Two matrix weighted inequalities for commutators with fractional integral operators

In this paper we prove two matrix weighted norm inequalities for the commutator of a fractional integral operator and multiplication by symbol. More precisely, extend recent results second author, Pott, Treil on commutators Calderon-Zygmund operators symbol to setting. particular, completely Bloom theory Holmes, Rahm, Spencer setting with also provide new arbitrary weights. These are even in scalar one