Trudinger-Moser type inequalities for weighted Sobolev spaces involving fractional dimensions

Abstract

We derive sharp Trudinger-Moser inequalities for weighted Sobolev spaces and prove the existence of extremal functions. The inequalities we obtain here extend for fractional dimensions the classical results in the radial case. The main ingredient used in our arguments reveals a new proof of a result due to J. Moser for which we give an improved version.