Lipschitz estimates for generalized commutators of fractional integrals with rough kernel

Let $ T ^{A} _{\Omega, \alpha} $ (0 < α < n ) be the generalized commutator generated by fractional integral with rough kernel and the m –th order remainder of the Taylor formula of a function A. In this paper, the ( L p , L r ) ( r > 1) boundedness, the weak ( L 1 , L n /( n – α – β ) ) boundedness and the ( L p , Ḟ β , ∞ p ) boundedness of $ T ^{A} _{\Omega, \alpha} $ are discussed, when D γ A belongs to the Lipschitz function spaces.