Abstract Working in the frame of variable bounded variation spaces sense Wiener, introduced by Castillo, Merentes, and Rafeiro, we prove convergence means classical convolution integral operators. In proposed approach, a crucial step is modulus smoothness for absolutely continuous functions. Several preliminary properties $$p(\cdot )$$ <...

In this paper Lq → Lp boundedness of integral operator with operator-valued kernels is studied and main result is applied to convolution operators.