We define a new class of positive and measurable functions that are bounded by regularly varying functions (which were introduced by Karamata). We study integrals and Laplace transforms of these functions. We use the obtained results to study the tail of convolutions of distribution functions. The results are extended to functions that are bounded by O-regularly varying functions.
CADENA, M., KRATZ, M. et OMEY, E. (2019). On functions bounded by Karamata functions. Journal of Mathematical Sciences, 237(5), pp. 621-630.