ON THE HAUSDORFF MEASURE OF SHRINKING TARGET SETS ON SELF?CONFORMAL SETS

In this article, we study the Hausdorff measure of shrinking target sets on self-conformal sets. The dimension are interested in here was established by Hill and Velani 1995 [Invent. Math. 119(1) (1995), 175–198]. However, until recently, little more known about these particular paper provide a complete characterisation sets, obtaining dichotomy for which is determined convergence or divergence sum depending radii our “shrinking targets”. Our main result complements earlier work Levesley, Salp, [Math. Ann. 338(1) (2007), 97–118], recent Baker Proc. Cambridge Philos. Soc. 167(3) (2019), 567–597] .