On a weighted Trudinger-Moser inequality in [formula omitted

Abstract

We establish the Trudinger-Moser inequality on weighted Sobolev spaces in the whole space, and for a class of quasilinear elliptic operators in radial form of the type Lu:=−r−θ(rα|u′(r)|βu′(r))′, where θ,β≥0 and α>0, are constants satisfying some existence conditions. It is worth emphasizing that these operators generalize the p-Laplacian and k-Hessian operators in the radial case. Our results involve fractional dimensions, a new weighted Pólya-Szegö principle, and a boundness value for the optimal constant in a Gagliardo-Nirenberg type inequality.