LAUSR

In this paper, the boundedness for higher order commutators of fractional integrals is obtained on variable exponent Herz–Morrey spaces $$ M\dot{K}_{p, q(\cdot )}^{\alpha (\cdot ), \lambda }(\mathbb {R}^{n})$$MK˙p,q(·)α(·),λ(Rn) applying some properties of variable exponent and $$\mathrm {BMO}$$BMO function, where $$\alpha (x)\in L^{\infty }(\mathbb {R}^{n})$$α(x)∈L∞(Rn) are log-Hölder continuous both at the origin and at infinity, and q(x) satisfies the logarithmic continuity condition.