A Trudinger-Moser inequality under a refined constraint in fractional dimensions and extremal functions

We establish a Trudinger-Moser type inequality with a Tintarev-type constraint in fractional-dimensional spaces and prove the existence of maximizers in the critical regime. Our results provide a refinement of those in (Calc. Var. 52 (2015), 125-163) in the setting of fractional-dimensional spaces, as well as of those in (Ann. Global Anal. Geom. 54 (2018), 237-256) for classical Sobolev spaces.