Convergence and Rate of Approximation in BVΦ for a Class of Integral Operators

We obtain estimates and convergence results with respect to ?-variation in spaces BV_Φ for a class of linear integral operators whose kernels satisfy a general homogeneity condition. Rates of approximation are also obtained. As applications, we apply our general theory to the case of Mellin convolution operators, to that one of moment operators and finally to a class of operators of fractional order.