Integral operators with rough kernels in variable Lebesgue spaces.

We study integral operators with kernels K (x , y) = k 1 (x - A 1 y) ⋯ k m (x - A m y) , k i (x) = Ω i (x) | x | n / q i where Ω i : R n → R are homogeneous functions of degree zero, satisfying a size and a Dini condition, Ai are certain invertible matrices, and n q 1 + ⋯ + n q m = n - α , 0 ≤ α < n . We obtain the boundedness of this operator from L p (·) into L q (·) for 1 q (·) = 1 p (·) - α n , for certain exponent functions p satisfying weaker conditions than the classical log-Hölder conditions. [ABSTRACT FROM AUTHOR]