In , the notion of homogeneous perfect sets as a generalization of Cantor type sets is introduced and their Hausdorff
and lower box-counting dimensions are studied. In this paper, we determine their exact packing and upper box-counting dimensions
based on the length of their fundamental intervals and the gaps between them. Some known results concerning the dimensions
of Cantor type sets are generalized.
We prove that the conjugate convolution operators can be used to calculate jumps for functions. Our results generalize the theorems established by He and Shi. Furthermore, by using Lukács and Móricz's idea, we solve an open question posed by Shi and Hu.