Extremal functions for singular Moser–Trudinger embeddings.

We study Moser–Trudinger type functionals in the presence of singular potentials. In particular we propose a proof of a singular Carleson–Chang type estimate by means of Onofri’s inequality for the unit disk in R 2 . Moreover we extend the analysis of Adimurthi (2004) and Csató and Roy (2015a) considering Adimurthi–Druet type functionals on compact surfaces with conical singularities and discussing the existence of extremals for such functionals. [ABSTRACT FROM AUTHOR]